UB 

290 

Us 


IC-NRLF 


72    551 


IT 


MANUAL 

FOR  THE  SOLUTION  OF 
MILITARY  CIPHERS 


BY 


PARKER  P^ITT 

Captain  of  Infantry,  U.  S.  A. 


PRESS  OF 

THE  ARMY  SERVICE  SCHOOLS 
Fort  Leavenworth,  Kansas 


1916 


u 


\ 


MANUAL  FOR  THE  SOLUTION 
OF  MILITARY  CIPHERS 

BY 

PARKER  HITT 

Captain  of  Infantry,  United  States  Army 


Introduction 

HE  history  of  war  teems  with  occasions  where  the  in- 
terception  of  dispatches  and  orders  written  in  plain 
language  has  resulted  in  defeat  and  disaster  for  the 
force  whose  intentions  thus  became  known  at  once  to  the  en- 
emy. For  this  reason,  prudent  generals  have  used  cipher 
*and  code  messages  from  time  immemorial.  The  necessity 
for  exact  expression  of  ideas  practically  excludes  the  use 
of  codes  for  military  work  although  it  is  possible  that  a 
special  tactical  code  might  be  useful  for  preparation  of  tac- 
tical orders. 

It  is  necessary  therefore  to  fall  back  on  ciphers  for  gen- 
eral military  work  if  secrecy  of  communication  is  to  be  fairly 
well  assured.  It  may  as  well  be  stated  here  that  no  prac- 
ticable military  cipher  is  mathematically  indecipherable  if 
intercepted;  the  most  that  can  be  expected  is  to  delay  for  a 
longer  or  shorter  time  the  deciphering  of  the  message  by  the 
interceptor. 

The  capture  of  messengers  is  no  longer  the  only  means 
available  to  the  enemy  for  gaining  information  as  to  the 
plans  of  a  commander.  All  radio  messages  sent  out  can  be 
copied  at  hostile  stations  within  radio  range.  If  the  enemy 
can  get  a  fine  wire  within  one  hundred  feet  of  a  buzzer  line 
or  within  thirty  feet  of  a  telegraph  line,  the  message  can  be 
copied  by  induction.  Messages  passing  over  commercial 
telegraph  lines,  and  even  over  military  lines,,  can  be  copied 
by  spies  in  the  offices.  On  telegraph  lines  of  a  permanent 
nature  it  is  possible  to  install  high  speed  automatic  sending 
and  receiving  machines  and  thus  prevent  surreptitious  copy- 
ing of  messages,  but  nothing  but  a  secure  cipher  will  serve 
with  other  means  of  communication. 


M150947 


It  is  not  alone  the  body  of  the  message  which  should  be 
in  cipher.  It  is  equally  important  that,  during  transmission, 
the  preamble,  place  from,  date,  address  and  signature  be 
enciphered;  but  this  should  be  done  by  the  sending  operator 
and  these  parts  must,  of  course,  be  deciphered  by  the  receiv- 
ing operator  before  delivery.  A  special  operators'  cipher 
should  be  used  for  this  purpose  but  it  is  difficult  to  prescribe 
one  that  would  be  simple  enough  for  the  average  operator, 
fast  and  yet  reasonably  safe.  Some  form  of  rotary  cipher 
machine  would  seem  to  be  best  suited  for  this  special  purpose. 

It  is  unnecessary  to  point  out  that  a  cipher  which  can 
be  deciphered  by  the  enemy  in  a  few  hours  is  worse  than 
useless.  It  requires  a  surprisingly  long  time  to  encipher 
and  decipher  a  message,  using  even  the  simplest  kind  of 
cipher,  and  errors  in  transmission  of  cipher  matter  by  wire 
or  radio  are  unfortunately  too  common. 

Kerckhoffs  has  stated  that  a  military  cipher  should  ful- 
fill the  following  requirements: 

1st.  The  system  should  be  materially,  if  not  mathemati- 
cally, indecipherable. 

2d.  It  should  cause  no  inconvenience  if  the  apparatus 
and  methods  fall  into  the  hands  of  the  enemy. 

3d.  The  key  should  be  such  that  it  could  be  communi- 
cated and  remembered  without  the  necessity  of  written  notes 
and  should  be  changeable  at  the  will  of  the  correspondents. 

4th.  The  system  should  be  applicable  to  telegraphic 
correspondence. 

5th.  The  apparatus  should  be  easily  carried  and  a 
single  person  should  be  able  to  operate  it. 

6th.  Finally,  in  view  of  the  circumstances  under  which 
it  must  be  used,  the  system  should  be  an  easy  one  to  operate, 
demanding  neither  mental  strain  nor  knowledge  of  a  long 
series  of  rules. 

A  brief  consideration  of  these  six  conditions  must  lead 
to  the  conclusion  that  there  is  no  perfect  military  cipher. 
The  first  requirement  is  the  one  most  often  overlooked  by 
those  prescribing  the  use  of  any  given  cipher  and,  even  if 
not  overlooked,  the  indecipherability  of  any  cipher  likely  to 
be  used  for  military  purposes  is  usually  vastly  overestimated 
by  those  prescribing  the  use  of  it. 

If  this  were  not  true,  there  would  have  been  neither  ma- 
terial for,  nor  purpose  in,  the  preparation  of  these  notes.  Of 
the  hundreds  of  actual  cipher  messages  examined  by  the 
writer,  at  least  nine-tenths  have  been  solved  by  the  methods 
to  be  set  forth.  These  messages  were  prepared  by  the 
methods  in  use  by  the  United  States  Army,  the  various  Mex- 
vi 


lean  armies  and  their  secret  agents,  and  by  other  methods  in 
common  use.  The  usual  failure  has  been  with  very  short 
messages.  Foreign  works  consulted  lead  to  the  belief  that 
many  European  powers  have  used,  for  military  purposes, 
cipher  methods  which  vary  from  an  extreme  simplicity  to 
a  complexity  which  is  more  apparent  than  real.  What  effect 
recent  events  have  had  on  this  matter  remains  to  be  seen.  It 
is  enough  that  the  cipher  experts  of  practically  every  Euro- 
pean country  have  appealed  to  the  military  authorities  of 
their  respective  countries  time  and  again  to  do  away  with 
these  useless  ciphers  and  to  adopt  something  which  offers 
more  security,  even  at  the  expense  of  other  considerations. 

The  cipher  of  the  amateur,  or  of  the  non-expert  who 
makes  one  up  for  some  special  purpose,  is  almost  sure  to 
fall  into  one  of  the  classes  whose  solution  is  an  easy  matter. 
The  human  mind  works  along  the  same  lines,  in  spite  of  an 
attempt  at  originality  on  the  part  of  the  individual,  and 
this  is  particularly  true  of  cipher  work  because  there  are  so 
few  sources  of  information  available.  In  other  words,  the 
average  man,  when  he  sits  down  to  evolve  a  cipher,  has 
nothing  to  improve  upon;  he  invents  and  there  is  no  one  to 
tell  him  that  his  invention  is,  in  principle,  hundreds  of  years 
old.  The  ciphers  of  the  Abbe  Tritheme,  1499,  are  the  basis 
of  most  of  the  modern  substitution  ciphers. 

In  view  of  these  facts,  no  message  should  be  considered 
indecipherable.  Very  short  messages  are  often  very  difficult 
and  may  easily  be  entirely  beyond  the  possibility  of  analysis 
and  solution,  but  it  is  surprising  what  can  be  done,  at  times, 
with  a  message  of  only  a  few  words. 

In  the  event  of  active  operations,  cipher  experts  will  be 
in  demand  at  once.  Like  all  other  experts,  the  cipher  expert 
is  not  born  or  made  in  a  day;  and  it  is  only  constant  work 
with  ciphers,  combined  with  a  thorough  knowledge  of  their 
underlying  principles,  that  will  make  one  worthy  of  the  name. 


Vll 


Chapter  I 


Equipment  for  Cipher  Work 

UCCESS  in  dealing  with  unknown  ciphers  is 
measured  by  these  four  things  in  the  order 
named;  perseverance,  careful  methods  of 
analysis,  intuition,  luck.  The  ability  at  least  to  read 
the  language  of  the  original  text  is  very  desirable  but 
not  essential. 

Cipher  work  will  have  little  permanent  attrac- 
tion for  one  who  expects  results  at  once,  without 
labor,  for  there  is  a  vast  amount  of  purely  routine 
labor  in  the  preparation  of  frequency  tables,  the 
rearrangement  of  ciphers  for  examination,  and 
the  trial  and  fitting  of  letter  to  letter  before  the 
message  begins  to  appear. 

The  methods  of  analysis  given  in  these  notes 
cover  only  the  simpler  varieties  of  cipher  and  it  is, 
of  course,  impossible  to  enumerate  all  the  varieties 
of  these.  It  is  believed  that  the  methods  laid  down 
are  sound  and  several  years  of  successful  work 
along  this  line  would  seem  to  confirm  this  belief. 
For  more  advanced  work  there  is  no  recourse  but  to 
study  the  European  authorities  whose  writings  are 
mostly  in  French,  German,  and  Italian  and,  unfor- 
tunately, are  rarely  available  in  English  translations. 

Under  intuition  must  be  included  a  knowledge 
of  the  general  situation  and,  if  possible,  the  special 
situation  which  led  to  the  sending  of  the  cipher 
message.  The  knowledge  or  guess  that  a  certain 
cipher  messages  contains  a  particular  word,  often 
leads  to  its  solution, 
l 


— 2— 

As  to  luck,  there  is  the  old  miner's  proverb: 
"Gold  is  where  you  find  it." 

The  equipment  for  an  office,  where  much  cipher 
work  is  handled,  will  now  be  considered.  The 
casual  worker  with  ciphers  can  get  along  with  much 
less,  but  the  methods  of  filing  and  keeping  a  record 
of  all  messages  studied  should  be  followed  wherever 
possible.  The  interchange  of  results  between  in- 
dividuals and  between  offices  should  be  encouraged 
and,  in  time  of  active  operations,  should  be  manda- 
tory. An  enemy  may  be  using  the  same  cipher  in 
widely  separated  parts  of  the  zone  of  operations  and 
it  is  useless  labor  to  have  many  cipher  offices  work- 
ing on  intercepted  messages,  all  in  the  same  cipher, 
when  one  office  may  have  the  solution  that  will 
apply  to  all  of  them. 

Cipher  work  requires  concentration  and  quiet 
and  often  must  proceed  without  regard  to  hours. 
The  office  should  be  chosen  with  these  points  in  mind. 
A  clerical  force  is  desirable  and  even  necessary  if 
there  is  much  work  to  do.  The  clerk  or  clerks  can 
soon  be  trained  to  do  the  routine  part  of  the  analysis. 

It  is  believed  that  each  Field  Army  should  have 
such  an  office  where  all  ciphers  intercepted  by  forces 
under  command  of  the  Field  Army  Commander 
should  be  sent  at  once  for  examination.  This  work 
naturally  falls  to  the  Intelligence  section  of  the  Gen- 
eral Staff  at  this  headquarters.  A  special  radio 
station,  with  receiving  instruments  only,  should  be 
an  adjunct  to  this  office  and  its  function  should  be 
to  copy  all  hostile  radio  messages  whether  in  cipher 
or  plain  text.  Such  a  radio  station  requires  but  a 
small  antenna;  one  of  the  pack  set  type  or  any 
amateur's  antenna  is  sufficient,  and  the  station  in- 
struments can  be  easily  carried  in  a  suit  case. 
Three  thoroughly  competent  operators  should  be 


— 3— 

provided,  so  that  the  station  can  be  "listening  in" 
during  the  entire  twenty-four  hours. 

The  office  should  be  provided  with  tables  of 
frequency  of  the  language  of  the  enemy,  covering 
single  letters  and  digraphs ;  a  dictionary  and  gram- 
mar of  that  language ;  copies  of  the  War  Department 
Code,  Western  Union  Code  and  any  other  available 
ones;  types  of  apparatus  or,  at  least,  data  on  appa- 
ratus and  cipher  methods  in  use  by  the  enemy ;  and 
a  safe  filing  cabinet  and  card  index  for  filing  mes- 
sages examined.  A  typewriter  is  also  desirable. 

The  office  work  on  a  cipher  under  examination 
should  be  done  on  paper  of  a  standard  and  uniform 
size.  Printed  forms  containing  twenty-six  ruled 
lines  and  a  vertical  alphabet  are  convenient  and 
save  time  in  preparation  of  frequency  tables.  Any 
new  cipher  methods  which  are  found  to  be  in  use 
by  the  enemy  should,  when  solved,  be  communicated 
to  all  similar  offices  in  the  Army  for  their  informa- 
tion. 

Unless  an  enemy  were  exceedingly  vigilant 
and  changed  keys  and  methods  frequently,  such  an 
office  would,  in  a  few  days,  be  in  a  position  to  dis- 
close completely  all  intercepted  cipher  communica- 
tions of  the  enemy  with  practically  no  delay. 


Chapter  II 


Principles  of  Mechanism  of  a  Written  Language 

ITH  a  few  exceptions,  notably  Chinese,  all  mod- 
ern  languages  are  constructed  of  words  which 
in  turn  are  formed  from  letters.  In  any  given 
language  the  number  of  letters,  and  their  conven- 
tional order  is  fixed.  Thus  English  is  written  with 
26  letters  and  their  conventional  order  is  A,  B,  C,  D, 
E,  etc.  Some  letters  are  used  very  frequently  and 
others  rarely,  In  fact,  if  ten  thousand  consecutive 
letters  of  a  text  be  counted  and  the  frequency  of  oc- 
currence of  each  letter  be  noted,  the  numbers  found 
will  be  practically  identical  with  those  obtained  from 
any  other  text  of  ten  thousand  letters  in  the  same 
language.  The  relative  proportion  of  occurrence  of 
the  various  letters  will  also  hold  approximately  for 
even  very  short  texts. 

Such  a  count  of  a  large  number  of  letters,  when 
it  is  put  in  the  form  of  a  table,  is  known  as  a  fre- 
quency table.  Every  language  has  its  own  dis- 
tinctive frequency  table  and,  for  any  given  language, 
the  frequency  table  is  almost  as  fixed  as  the  alpha- 
bet. There  are  minor  differences  in  frequency  tables 
prepared  from  texts  on  special  subjects.  For  ex- 
ample, if  the  text  be  newspaper  matter,  the  fre- 
quency table  will  differ  slightly  from  one  prepared 
from  military  orders  and  will  also  differ  slightly 
from  one  prepared  from  telegraph  messages.  But 
these  differences  are  very  slight  as  compared  with 
the  differences  between  the  frequency  tables  of  two 
different  languages. 

Again  there  is  a  fixed  ratio  of  occurrence  of 

4 


every  letter  with  every  other  for  any  language  and 
this,  put  in  table  form,  constitutes  a  table  of  fre- 
quency of  digraphs.  In  the  same  way  a  table  of 
trigraphs,  showing  the  ratio  of  occurrence  of  any 
three  letters  in  sequence,  could  be  prepared,  but 
such  a  table  would  be  very  extensive  and  a  count  of 
the  more  common  three  letter  combinations  is 
usually  used. 

Other  tables,  such  as  frequency  of  initial  and 
final  letters  of  words,  might  be  of  value  but  the 
common  practice  is  to  put  cipher  text  into  groups 
of  five  or  ten  letters  each  and  eliminate  word  forms. 
This  is  almost  a  necessity  in  telegraphic  and  radio 
communication  to  enable  the  receiving  operator  to 
check  correct  receipt  of  a  message.  He  must  get 
five  letters,  neither  more  nor  less,  per  word  or  he  is 
sure  a  mistake  has  been  made.  There  is  little  diffi- 
culty, as  a  rule,  in  restoring  word  forms  in  the 
deciphered  message. 

We  will  now  take  up,  in  order,  the  various 
frequency  tables  and  linguistic  peculiarities  of 
English  and  Spanish.  Frequency  tables  for  French, 
German,  and  Italian  for  single  letters  will  follow. 
All  frequency  tables  have  been  re-calculated  from 
at  least  ten  thousand  letters  of  text  and  compared 
with  existing  tables.  No  marked  difference  has 
been  found  in  any  case  between  the  re-calculated 
tables  and  those  already  in  use. 

Data  for  Solution  of  Ciphers  in  English 

TABLE  I. — Normal  frequency  table.  Frequency 
for  ten  thousand  letters  and  for  two  hundred  let- 
ters. This  latter  is  put  in  graphic  form  and  is 
necessarily  an  approximation.  Taken  from  mili- 
tary orders  and  reports,  English  text. 


— 6— 

10,000  Letters  200  Letters 

A          778  16  1111111111111111 

B          141  3  111 

C          296  6  111111 

D          402  8  11111111 

E          1277  26  11111111111111111111111111 

F          197  4  1111 

G          174  3  111 

H          595  12  111111111111 

I           667  13  1111111111111 

J           51  11 

K           74  2  11 

L          372  7  1111111 

M          288  6  111111 

N          686  14  11111111111111 

0          807  16  1111111111111111 

P          223  4  1111 
Q            8 

R          651  13  1111111111111 

S           622  12  111111111111 

T          855  17  11111111111111111 

U          308  6  111111 

V          112  2  11 

W          176  3  111 
X           27 

Y          196  4  1111 
Z           17 

Vowels  AEIOU  =  38.37%;  consonants  LNRST=31.86% ; 
consonants  JKQXZ  =  1.77%. 

The  vowels  may  be   safely  taken   as   40%,   consonants 
LNRST  as  30%  and  consonants  JKQXZ  as  2%. 

Order  of  letters:  ETOANIRSHDLUCMPF 
YWGBVKJXZQ. 

TABLE  II. — Frequency  table  for  telegraph  mes- 
sages, English  text.  This  table  varies  slightly  from 
the  standard  frequency  table  because  the  common 
word  "the"  is  rarely  used  in  telegrams  and  there  is 
a  tendency  to  use  longer  and  less  common  words  in 
preparing  telegraph  messages. 


10,000  Letters  200  Letters 

A  813  16  1111111111111111 

B  149  3  111 

C  306  6  111111 

D  417  8  11111111 

E  1319  26  11111111111111111111111111 

F  205  4  1111 

G  201  4  1111 

H  386  8  11111111 

I  711  14  11111111111111 

J  42  11 

K  88  2  11 

L  392  8  11111111 

M  273  6  111111 

N  718  14  11111111111111 

0  844  17  11111111111111111 

P  243  5  11111 

Q  38  11 

R  677  14  11111111111111 

S  656  13  1111111111111 

T  634  13  1111111111111 

U  321  6  111111 

V  136  3  111 

W  166  3  111 

X  51  11 

Y  208  4  1111 

Z  6 

In  this  table  the  vowels  AE  1011=40.08%,  consonants 
LNRST  =  30.77%  and  consonants  JKQXZ  =  2.25%. 

Orders  of  letters:  EOANIRSTDLHUCMP 
YFGWBVKXJQZ. 

TABLE  III. — Table  of  frequency  of  digraphs, 
duals  or  pairs  (English) .  This  table  was  prepared 
from  20,000  letters,  but  the  figures  shown  are  on 
the  basis  of  2,000  letters.  For  this  reason  they  are, 
to  a  certain  extent,  approximate;  that  is,  merely 
because  no  figures  are  shown  for  certain  combina- 
tions, we  should  not  assume  that  such  combinations 
never  occur  but  rather  that  they  are  rare.  The 
letters  in  the  horizontal  line  at  the  top  and  bottom 
are  the  leading  letters ;  those  in  the  vertical  columns 
at  the  sides  are  the  following  letters.  Thus  in  two 
thousand  letters  we  may  expect  to  find  AH  once  and 
HA  twenty-six  times. 


ABODE 

F  G 

HI    J   K  L  M 

N   0 

P 

Q    R    S  T  U   V  W  X  Y  Z 

A 

1|   7 

10 

22 

3 

2|26 

4 

2 

2 

7 

8 

11 

2 

9|      |13|12|  9 

2 

4 

1 

12  1 

B 

b 

1 

2| 

I 

1 

1 

1 

1 

2 

2|   1 

3 

JJ 

(J 

6 

1|   1|14|   2|      [      |H| 

1111   3 

2|   3|   1 

1| 

1 

1 

D 

6 

|12|30|   1| 

2| 

4|      |30|   1 

4|   1|   1 

11 

1 

3 

E 

|11|14|16|12|   2|   6|33|10|  2|   6|18|14|12 

1 

7|      |36 

11 

12 

2 

16|   5 

1 

1 

F 

3| 

1   2|   8|   2|   1| 

2|      I 

2 

11   3 

25|      | 

3 

1 

1 

1 

Gr 

4 

1|   3 

2 

|11 

2 

3 

1 

H 

1 

11 

2 

4 

1 

4 

1| 

2 

1 

1| 

2 

10 

50 

3 

2 

1 

2|   1 

4 

12 

6 

5 

1 

12 

1 

5|  91  8|12|   1 

_3j      |12|13|22 

2|   3|   6 

1|   1| 

J 

1   11      1  ' 

1      1 

— 

K 

1| 

1| 

2| 

I 

2    11      1  11 

L     |14|   6|   2|   1|   6|   1|   1|   1|   6| 

9| 

3|   6 

3 

3|  2 

3 

5 

M    |   7| 

1   3|13|   2| 

2|   3| 

4|    1|10| 

4|   1 

1 

2 

N    |38| 

3|25| 

2 

1 

31 

3| 

2|   2|39| 

4|   3 

|H 

2 

O     |  1|   1|12|  4|  8|  8|  3|12|18 

2 

4|   7|   8|   3|   7 

|13|15|22| 

2|   6 

1|   5| 

P 

2| 

1|   8| 

1 

1| 

2|   4|   2|   3|   2| 

1|   8|   1|   4 

3|   1| 

Q 

u 

I 

1   1|   11      1 

1 

R    |16|   1|   3|   3|40|   3|   6 

2|   6| 

1|   2|   1|25 

HI 

2    2 

8 

11 

2 

S 

16 

1 

3 

25|   1 

2 

1  '< 

11  2 

1 

12|   7|   2| 

9 

11 

6 

11 

1 

G 

T 

25)   1 

3 

12 

13|   5 

2 

3 

20 

2 

1|24|   8|   2]      |16 

20 

11|   6 

2 

2 

7 

U 

11   2 

H  6 

1|  3 

2 

2 

3| 

3|  1 

|17 

1 

5|   3|   5|   5| 

1| 

V 

3|   1| 

51 

| 

6| 

1   31 

2| 

1   5| 

1 

w 

1 

2|   8 

1|   11 

1 

1 

2 

4| 

2 

3 

3| 

X 

1 

4 

2 

11 

1 

y 

3 

2 

2 

4 

1 

1 

8 

1|   2 

11 

3 

1 

7 

z 

1| 

1 

1 

ABCDEFGHI  JKLMNOPQ  RSTUVWXYZ 


TABLE  IV. — Order  of  frequency  of  common 
pairs  to  be  expected  in  a  count  of  2,000  letters  of 
military  or  semi-military  English  text.  (Based  on 
a  count  of  20,000  letters) . 


TH 
ER 
ON 

AN 
RE 
HE 
IN 
ED 
ND 
HA 


50 
40 
39 
38 
36 
33 
31 
30 
30 
26 


AT 

EN 
ES 
OF 
OR 
NT 
EA 

TI 
TO 

IT 


25 
25 
25 
25 
25 
24 
22 
22 
22 
20 


ST 
IO 
LE 

IS 

ou 

AR 
AS 
DE 
RT 
VE 


20 
18 
18 
17 
17 
16 
16 
16 
16 
16 


TABLE  V. — Table  of  recurrence  of  groups  of 

three  letters  to  be  expected  in  a  count  of  10,000 
letters   of  English  text. 

THE     89                        TIO     33  EDT 

54                      FOR     33  TIS 

47                      NDE     31  OFT 

39                      HAS     28  STH 

36                       NCE     27  MEN 


AND 
THA 
ENT 
ION 


27 
25 
23 
21 
20 


TABLE  VI. — Table  of  frequency  of  occurrence 
of  letters  as  initials  and  finals  of  English  words. 
Based  on  a  count  of  4,000  words;  this  table  gives 
the  figures  for  an  average  100  words  and  is  neces- 
sarily an  approximation,  like  Table  III.  English 
words  are  derived  from  so  many  sources  that  it  is 
not  impossible  for  any  letter  to  occur  as  an  initial  or 
final  of  a  word,  although  Q,  X  and  Z  are  rare  as 
initials  and  B,I,  J,  Q,  V,  X  and  Z  are  rare  as  finals. 

Letters  ABCDEFGHIJKLMNOPQRSTUVWXYZ 
Initial  96652423311242  10  2-45  17  2-7  -  3  - 
Final  1  --1017642--161941-  89111  -  1  -  8  - 

It  is  practically  impossible  to  find  five  consec- 
tive  letters  in  an  English  text  without  a  vowel  and  we 
may  expect  from  one  to  three  with  two  as  the  gen- 
eral average.  In  any  twenty  letters  we  may  ex- 
pect to  find  from  6  to  9  vowels  with  8  as  an  average. 
Among  themselves  the  relative  frequency  of  occur- 
rence of  each  of  the  vowels,  (including  Y  when  a 
vowel)  is  as  follows: 

A,  19.5%  E,  32.0%  I,    16.7% 

0,  20.2%  U,     8.0%  Y,     3.6% 

The  foregoing  tables  give  all  the  essential  facts 
about  the  mechanism  of  the  English  language  from 
the  standpoint  of  the  solution  of  ciphers.  The  use 
to  be  made  of  these  tables  will  be  evident  when  the 
solution  of  different  types  of  ciphers  is  taken  up. 

Data  for  the  Solution  of  Ciphers  in  Spanish 

The  Spanish  language  is  written  with  the  fol- 
lowing alphabet: 

ABCCHDEFGHIJLLL 
MNNOPQRRRSTUVXYZ 

while  the  exact  sense  often  depends  upon  the  use  of 
accents  over  the  vowels.  However,  in  cipher  work 
it  is  exceedingly  inconvenient  to  use  the  permanent 
digraphs,  CH,  LL  and  RR  and  they  do  not  appear  as 
such  in  any  specimens  of  Spanish  or  Mexican  cipher 


—10— 

examined.  Accented  vowels  and  N  are  also  not 
found  and  we  may,  in  general,  say  that  a  cipher 
whose  text  is  Spanish  will  be  prepared  with  the  fol- 
lowing alphabet : 

A  B  CD  EFGHIJLMNOPQRSTUVXYZ 
and  the  receiver  must  supply  the  accents  and  the 

tilde  over  the  N  to  conform  to  the  general  sense. 

However,  many  Mexican  cipher  alphabets  con- 
tain the  letters  K  and  W.  This  is  particularly  true 
of  the  ciphers  in  use  by  secret  service  agents  who 
must  be  prepared  to  handle  words  like  NEW  YORK, 
WILSON  and  WASHINGTON.  The  letters  K  and 
W  will,  however,  have  a  negligible  frequency  except 
in  short  messages  where  words  like  these  occur  more 
than  once. 

In  this  connection,  if  a  cipher  contains  Mex- 
ican geographical  names  like  CHIHUAHUA,  MEX- 
ICO, MUZQUIZ,  the  letters  H,  X  and  Z  will  have  a 
somewhat  exaggerated  frequency. 

In  Spanish,  the  letter  Q  is  always  followed  by 
U  and  the  U  is  always  followed  by  one  of  the  other 
vowels,  A,  E,  I  or  O.  As  QUE  or  QUI  occurs  not 
infrequently  in  Spanish  text,  particularly  in  tele- 
graphic correspondence,  it  is  well  worth  noting  that, 
if  a  Q  occurs  in  a  transposition  cipher,  we  must  con- 
nect it  with  U  and  another  vowel.  The  clue  to  sev- 
eral transposition  ciphers  has  been  found  from  this 
simple  relation. 

TABLE  VII. — Normal  frequency  table  for  mili- 
tary orders  and  reports,  calculated  on  a  basis  of 
10,000  letters  of  Spanish  text.  The  graphic  form  is 
on  a  basis  of  200  letters. 


—11— 

10,000  Letters  200  Letters 

A  1352  27  111111111111111111111111111 

B  102  2  11 

C  474  9  111111111 

D  524  10  1111111111 

E  1402  28  1111111111111111111111111111 

F  91  2  11 

G  137  3  111 

H  102  2  11 

I  606  12  111111111111 

J  41  11 

L  517  10  1111111111 

M  300  6  111111 

N  619  12  111111111111 

0  818  16  1111111111111111 

P  257  5  11111 

Q  87  2  11 

R  751  15  111111111111111 

S  724  14  11111111111111 

T  422  8  11111111 

U  387  7  1111111 

V  85  2  11 

X  6 

Y  103  2  11 

Z  42  11 

In  this  table  the  vowels   AEIOU=:45.65% ;   consonants 
LNRST  =  30.33%;  consonants  JKQXZ  =  1.76%. 

Order  of  letters: 
EAORSNIDLCTUMPGY  (BH)   F  Q  V  Z  J  X. 

TABLE  VIII. — Table  of  frequency  of  digraphs, 
duals  or  pairs,  Spanish  text.  Like  Table  III,  this 
table  is  on  the  basis  of  2,000  letters  although  pre- 
pared from  a  count  of  20,000  letters.  For  this  reason 
it  is,  to  a  certain  extent  an  approximation;  that  is, 
merely  because  no  figures  are  shown  for  certain  com- 
binations, we  should  not  assume  that  such  combina- 
tions never  occur  but  rather  that  they  are  rare.  The 
letters  in  the  horizontal  lines  at  the  top  and  bottom 
are  the  leading  letters ;  those  in  the  vertical  columns 
at  the  sides  are  the  following  letters.  Thus,  in  two 
thousand  letters,  we  may  expect  to  find  AI  twice  and 
IA  twenty-three  times. 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 


—12— 


ABODE    FGH    IJ    LMNO    PQR    STUV    XYZ 


A 

91 

4|19|11|   5| 

6|17|23|      |54|18|   9|   3|20|      |29|11|21|   8 

6|         2 

5|       A 

B       |   6| 

3| 

11         4|                  | 

I 

B 

C       |24| 

6|   6|24| 

5|         3| 

8|   8| 

9|   5| 

2| 

2| 

C 

D 

31| 

|29|      ! 

3|     . 

19|13|             10|   9| 

I 

4| 

D 

E 

12|   2|   6|59|10| 

1     5|   7    2  12|18 

22|   4 

9        38|25|28|25 

8 

3| 

E 

F 

4 

4| 

4| 

3| 

1   3|      | 

11 

F 

G 

2| 

4 

8 

1   4|                       | 

2 

G 

H 

2| 

|12|      |10 

I 

1   2| 

1         11 

H 

I 

S 

|23|16 

5|   2| 

3 

11 

13|                     6!lO|  5| 

3| 

1 

J 

1 

1      1 

2| 

1|                       1 

J 

L 

21|   8|   6|      |89|   3|   3| 

7        21| 

5|   6| 

121   2| 

2 

L 

M 

12  1 

6|      1 

6|         1| 

6|15| 

7|   2| 

6 

1| 

M 

N       |32| 

1      |46|      |   2 

8| 

32 

I 

12 

2|      |       N 

0       | 

|26|22|   2|   6|   3 

4 

9 

16 

2 

8        ct 

.0        15|   7 

11 

O 

P       |13 

1113 

| 

2 

4|   9|   2|   7| 

41111 

P 

Q       |H 

S 

2| 

3|   1| 

Q 

R 

40| 

I 

|27|   2| 

4 

4 

36  1 

3        111      |17|   3 

R 

S 

39| 

|52| 

10 

7  14| 

21 

114 

3 

S 

T 

51 

1      1      U3| 

4 

4 

18|   5| 

61301 

T 

U 

2| 

1   4|   2|   6|   3|   4| 

1   5| 

2|   6| 

4|17       |15 

2| 

1 

U 

=5 

V 

2| 

1      1      1   2|      | 

2|      I         2 

1   2 

2 

I 

X 

I 

1 

Y 

5 

6 

2 

1   5| 

2 

21      Y 

Z 

11 

2 

'  1      1 

11      1 

1      i    4| 

1   2 

1 

Z 

ABODE 

F 

o 

HIJLMNOPQRS 

T  U 

V    X  Y  Zj 

TABLE  IX. — Order  of  frequency  of  common 
pairs  to  be  expected  in  a  count  of  2,000  letters  of 
Spanish  military  orders  and  reports.  Based  on 
Table  VIII. 


DE  59 

LA  54 

ES  52 

EN  46 

AR  40 

AS  39 

EL  39 

RE  38 

OR  36 

AN  32 


ON  32 

AD  31 

ST  30 

ED  29 

RA  29 

TE  28 

ER  27 

CO  26 

SE  25 

UE  25 


AC  24 

EC  24 

CI  23 

IA  23 

DO  22 

NE  22 

AL  21 

LL  21 

PA  20 

PO  20 


—13— 

Alphabetic  Frequency  Tables 
(Truesdell) 

Frequency  of  occurrence  in  1,000  letters  of  text : 

Letter  French  German    Italian    Portuguese 

A  80  52  117  140 

B  6  18  6  6 

C  33  31  45  34 

D  40  51  31  40 

E  197  173  126  142 

F  9  21  10  12 

G  7  42  17  10 

H  6  41  6  10 

I  65  81  114  59 

J  3  1  *  5 

K  10  * 

L  49  28  72  32 

M  31  20  30  46 

N  79  120  66  48 

O  57  28  93  110 

P     .  32  8  30  28 

Q  12  3  16 

R  74  69  64  64 

S  66  57  49  88 

T  65  60  60  43 

U  62  51  29  46 

V  21  9  20  15 

W  15 

X  3  *  1 

Y  2  *  1 

Z  1  14  12  4 
*  Occurrence  rare,  usually  in  proper  names. 

Order  of  Frequency 

French 

EANRSIUOLDCPMVQFGBJYZ 
T  HX 

German 

ENIRTSADGHCLFMBWZKVPJQXY 
U  O 

Italian 

EAIOLNRTSCDMUVGZFBQ 

P  H 

Portuguese 

EAOSRINMTDCLPQVFGBJZXY 
U  H 


—14— 


Graphic  Frequency  Tables 


Frequency  of  occurrence  in  200  letters  of  text. 

French 

A  16  1111111111111111 

B  2  11 

C  6  111111 

D  10  1111111111 

E  39  111111111111111111111111111111111111111 

F  2  11 
Gil 

H  1  1 

I  13  1111111111111 

J  1  1 
K 

L  10  1111111111 

M  6  111111 

N  16  1111111111111111 

0  11  11111111111 
P  6  111111 

Q  2  11 

R  15  111111111111111 

S  13  1111111111111 

T  13  1111111111111 

U  12  111111111111 

V  4  1111 

W 

X  1  1 

Y 

Z 

Italian 

A  23  11111111111111111111111 

B  1  1 

C  9  111111111 

D  6  111111 

E  25  1111111111111111111111111 

F  2  11 

G  3  111 

H  1  1 

1  23  11111111111111111111111 
L  14  11111111111111 

M  6  111111 

N  13  1111111111111 

0  19  1111111111111111111 

P  6  111111 


13  1111111111111 

S  10  1111111111 

T  12  111111111111 

U  6  111111 

V  4  1111 
X 
Y 

Z  2  11 


-15- 

German 

A  10  1111111111 

B  4  1111 

C  6  111111 

D  10  1111111111 

E  32  11111111111111111111111111111111 

F  4  1111 

G  8  11111111 

H  8  11111111 

I  16  1111111111111111 
J 

K  2  11 

L  6  111111 

M  4  1111 

N  24  111111111111111111111111  ' 

0  6  111111 
P  2  11 

R  14  11111111111111 

S  11  11111111111 

T  12  111111111111 

U  10  1111111111 

V  2  11 

W  3  111 

X 

Y 

Z  3  111 

Portuguese 

A  28  1111111111111111111111111111 

B  1  1 

C  7  1111111 

D  8  11111111 

E  28  1111111111111111111111111111 

F  2  11 

G  2  11 

H  2  11 

1  12  111111111111 
J  1  1 

L  6  111111 

M  9  111111111 

N  10  1111111111 

0  22  1111111111111111111111 

P  6  111111 

Q  3  111 

R  13  1111111111111 

S  18  111111111111111111 

T  9  111111111 

U  9  111111111 

V  3  111 

X 

Y 

Z  1  1 


Chapter  III 

Technique  of  Cipher  Examination 

IN  time  of  active  operations  it  is  important  that 
captured  or  intercepted  cipher  messages  reach 
the  examining  office  with  the  least  possible  de- 
lay.    The  text  of  messages,  captured  at  a  distance 
from  the  examining  office,  should  be  sent  to  the  office 
by  telegraph  or  telephone,  the  original  messages  be- 
ing forwarded  to  the  office  as  soon  thereafter  as 
possible. 

The  preamble,  "place  from,"  date,  address  and 
signature,  give  most  important  clues  as  to  the  lan- 
guage of  the  cipher,  the  cipher  method  probably 
used,  and  even  the  subject  matter  of  the  message. 
If  the  whole  of  a  telegraphic  or  radio  message  is  in 
cipher,  it  is  highly  probable  that  the  preamble,  "place 
from."  etc.,  are  in  an  operators'  cipher  and  are  dis- 
tinct from  the  body  of  the  message.  As  these  opera- 
tors' ciphers  are  necessarily  simple,  an  attempt 
should  always  be  made  to  discover,  by  methods  of 
analysis  to  be  set  forth  later,  the  exact  extent  of  the 
operator's  cipher  and  then  to  decipher  the  parts  of 
the  messages  enciphered  with  it. 

In  military  messages,  we  almost  invariably  find 
the  language  of  the  text  to  be  that  of  the  nation  to 
which  the  military  force  belongs.  The  language  of 
the  text  of  the  message  of  secret  agents  is,  however, 
another  matter  and,  in  dealing  with  such  messages, 
we  should  use  all  available  evidence,  both  external 
and  internal,  before  deciding  finally  on  the  language 
used.  Whenever  a  frequency  table  can  be  prepared, 

16 


—17— 

such  a  table  will  give  the  best  evidence  for  this  pur- 
pose. 

All  work  in  enciphering  and  deciphering  mes- 
sages and  in  copying  ciphers  should  be  done  with 
capital  letters.  There  is  much  less  chance  of  error 
when  working  with  capitals  and,  with  little  practice, 
it  is  just  about  as  fast.  An  additional  safeguard  is 
to  use  black  ink  or  pencil  for  the  plain  text  and 
colored  ink  or  pencil  for  the  cipher.  A  separate 
color  may  be  used  for  the  key  when  necessary. 

The  following  blank  form  is  suggested  as  con- 
venient for  keeping  a  record  of  a  cipher  under  exam- 
ination. It  should  accompany  the  cipher  through 
the  examining  process  and  should  be  filled  in  as  the 
facts  are  determined.  This  record,  the  original 
cipher  and  all  notes  of  work  done  during  the  exam- 
ination, should  be  filed  together  when  the  examina- 
tion is  completed,  whether  the  cipher  has  been  solved 
or  not.  It  may  be  that  other  ciphers  solved  later 
will  give  clues  to  the  solution  of  such  unsolved 
ciphers. 

The  first  column  of  this  blank  should  be  filled 
out  from  data  furnished  by  the  officer  obtaining 
the  cipher  from  the  enemy.  A  general  order,  em- 
phasizing the  importance  of  promptly  forwarding 
captured  or  intercepted  ciphers  to  an  examining 
office,  could  specify  that  a  brief  report  embodying 
this  data  should  be  forwarded  with  each  cipher. 

The  second  column  of  the  blank  should  be  filled 
out  progressively  as  the  work  proceeds.  The  office 
number  should  be  a  serial  one,  the  first  cipher  ex- 
amined being  No.  1.  The  date  and  hour  of  receipt 
at  examining  office  will  be  a  check  as  to  the  time 
required  to  transmit  it  from  place  of  capture.  The 
spaces  "From"  "At,"  "To,"  "At,"  "Date,"  are  for 


—18— 

the  information  concerning  sender  and  addressee 
of  the  cipher  and  are  to  be  obtained  from  the  mes- 
sage. In  case  an  operators'  cipher  has  been  used, 
these  parts  of  the  message  will  have  to  be  deciphered 
before  the  blanks  can  be  filled  in. 

Intelligence    Section,    General    Staff 
1st  Field  Army 


Place,  Date 

Record  of  Cipher  Examination 

This    cipher    obtained    by  Office    No.     

Received     . 


(Date)          (Hour) 

From 

at    

At     

on 

(date)  (hour)  To    __ 

How   being   transmitted   when   obtained.      At    

(Underscore    means    used    and    enter 

data    on    sending    and    receiving    sta-     Date    

tions ) . 

Sending  Receiving 

Station  Station         Probable    language    of    text 

Radio  (''Transposition- 

Telephone  r, 

ss  "I  Substitution 
Telegraph 


Buzzer 

Case 

Helio 

Remarks  : 
Lantern 

Flag 

Cyclist  from  to  Solution   completed   

.   '  (date)  (hour) 

Foot   Messenger 

Language    of    text    

Mtd.    Messenger 

Key,    (if  determined)    

How      obtained.      (Underscore     means 

used).      Captured    before    delivery    to     

addressee.     Captured     after     delivery 

to     addressee.     Intercepted,     not     re-      Type File  No. 

ceived      by      addressee.     Copied,      but 

received    by    addressee. 


REMARKS : 

Examiner. 

The  probable  language  of  the  text  is  assumed 
from  the  preceding  data  and,   if  necessary,  from 


—19— 

internal  evidence.  Thus  a  cipher  from  a  Mexican 
source  and  not  containing  K  or  W  is  probably  in 
Spanish. 

The  class  and  case  are  determined  by  the  rules 
laid  down  later.  The  space  for  remarks  is  to  per- 
mit notation  of  any  special  features.  When  the 
solution  is  completed,  the  date  and  hour  are  noted, 
the  language  of  text  and  key  (if  determined)  are 
entered  and  a  type  number,  to  identify  it  with  other 
ciphers  prepared  by  the  same  method  (but  not 
necessarily  the  same  key),  is  given  to  it.  The  file 
number  is  for  convenience  in  filing  and  in  prepara- 
tion of  a  card  index. 

The  process  of  examination  in  an  office  with  one 
examiner,  one  stenographer  and  one  clerk,  might  be 
as  follows :  On  receipt  of  a  captured  cipher  with 
accompanying  report,  the  stenographer  makes  four 
copies  of  the  cipher  on  the  typewriter.  The  clerk 
and  stenographer  then  check  the  work.  The  steno- 
grapher then  proceeds  to  fill  out  the  first  column  and 
first  two  lines  of  the  second  column  of  the  record 
blank  from  the  report  of  the  capturing  officer,  keep- 
ing the  original  cipher  and  two  copies  with  the 
record.  He  may  also  fill  out  the  first  seven  lines  of 
the  second  column,  if  this  data  is  on  the  captured 
cipher  in  plain  text.  In  the  meantime  the  clerk  is 
counting  and  setting  down  the  whole  number  of 
letters  of  the  cipher  and  the  occurrence  of  AEIOU, 
LNRST,  and  JKQXZ,  while  the  examining  officer 
is  looking  over  the  cipher  for  possible  recurring 
groups  of  letters  and  underlining  them  when  found. 

This  work  being  completed,  the  examining  officer 
is  in  a  position,  ordinarily,  to  decide  on  the  class  of 
the  cipher  and  he  may  have  found  something  in  his 
examination  which  will  lead  him  to  the  case  under 
the  class.  The  clerk  in  this  preliminary  count  should 


-20- 

keep  track  of  the  total  occurrence  of  each  of  the 
fifteen  check  letters  and  not  of  the  three  groups 
given  above.  This  takes  a  little  longer  but  when 
done,  the  data  for  fifteen  letters  of  the  alphabet  for 
a  frequency  table  is  completed,  leaving  only  eleven 
other  letters,  and  in  Spanish,  but  nine,  to  be  counted, 
in  case  it  is  necessary  to  prepare  a  frequency  table. 

If  the  examining  officer  decides  the  cipher  to 
be  of  the  transposition  class,  no  further  work  with 
frequency  tables  is  necessary.  The  clerk  should  pro- 
ceed to  count  and  set  down  the  number  of  vowels  in 
each  line  and  column  and  the  examining  officer  should 
look  for  any  occurrence  of  the  letter  Q  and  try  to 
connect  it  with  U  and  another  vowel.  The  steno- 
grapher may  be  set  to  work  putting  the  cipher  into 
rectangles  of  different  dimensions.  The  clerk's  work 
gives  data  for  possible  rearrangement,  for  if  the 
vowels  are  much  out  of  proportion  at  any  point,  they 
must  be  connected  with  the  proper  proportion  of 
consonants  as  a  first  step  in  rearrangement.  Work 
with  transposition  ciphers  must  necessarily  include 
much  of  the  fit  and  try  method.  The  details  of  this 
work  are  taken  up  later. 

If  a  cipher  seems  to  be  a  substitution  cipher, 
the  examining  officer  should  look  over  the  frequency 
of  occurrence  of  each  of  the  fifteen  letters  counted. 
If  some  letters  (it  is  of  no  importance  at  present 
which  ones)  occur  much  more  frequently  than  others 
and  some  occur  rarely  or  not  at  all,  we  may  safely 
decide  on  Case  4,  5  or  6  and  let  the  clerk  proceed  to 
finish  the  frequency  table  for  the  message.  On  the 
other  hand,  if  all  the  fifteen  letters  examined  occur 
with  somewhere  near  the  same  frequency — for  ex- 
ample, the  most  common  letter  occurring  not  over 
three  or  four  times  as  often  as  the  least  common 
letter — we  may  at  once  eliminate  the  first  three  cases 


—21— 

and  let  the  clerk  proceed  to  examine  the  cipher  for 
recurring  pairs  and  groups,  counting  the  intervening 
letters,  so  that  the  examining  officer  may  decide 
whether  Case  7,  or  some  more  complicated  case, 
should  be  chosen. 

If  something  more  complicated  than  Case  7  has 
been  used  and  other  ciphers  are  on  hand  awaiting 
examination,  the  cipher  should  go  into  the  unsolved 
file  to  be  worked  on  when  other  work  permits,  unless 
the  contents  of  the  cipher  are  believed  to  be  very  im- 
portant. Every  opportunity  should  be  taken  to  clean 
up  the  unsolved  file  and,  whenever  a  message  is 
solved,  the  methods  should  be  tried,  if  applicable,  to 
everything  remaining  in  the  file. 

The  first  few  days  or  weeks  after  the  establish- 
ment of  an  examining  office  will  be  the  most  trying 
time.  When  solved  ciphers  begin  to  pile  up,  the 
methods  of  the  enemy  will  be  more  and  more  appar- 
ent and  it  will  often  be  possible  to  determine  the 
method  from  knowledge  of  the  name  of  the  sender 
and  receiver. 

When  a  cipher  has  been  solved,  the  solution 
should  be  prepared  in  triplicate  and  given  the  serial 
number  of  the  cipher.  Any  parts  which  are  not 
clear,  through  errors  in  enciphering  or  in  transmis- 
sion, should  be  underlined  or  otherwise  made  con- 
spicuous, so  that  the  head  of  the  Intelligence  Section 
may  note  them  and,  possibly,  from  other  sources, 
supply  the  deficiency. 

One  of  the  copies  of  the  cipher  and  report  of 
examination,  with  a  copy  of  the  solution,  should  be 
turned  over  at  once  to  the  head  of  the  Intelligence 
Section  or  to  the  Chief  of  Staff.  The  other  copies  of 
the  solution  should  be  filed  with  the  original  cipher, 
the  report  of  examination,  and  all  work  done  on  the 
cipher. 


—22— 

Periodically,  say  once  a  week  or  even  daily  at 
the  begining  of  active  operations,  there  should  be  an 
interchange  between  all  examining  offices  of  solved 
messages  involving  new  methods  used  by  the  enemy. 
All  the  examining  offices  will  thus  be  kept  in  touch. 
It  may  also  be  possible  to  assign  certain  hostile  radio 
stations  to  each  examining  office  to  prevent  duplica- 
tion of  work. 


Chapter  IV 


Classes  of  Ciphers 

are,  in  general,  two  classes  of  ciphers. 
These  are  the  transposition  cipher  and  the 
substitution  cipher. 

Substitution  ciphers  may  be  made  up  of  sub- 
stituted letters,  numerals,  conventional  signs  or 
combinations  of  all  three;  and  furthermore,  for  a 
single  letter  of  the  original  text  there  may  be  substi- 
tuted a  single  letter,  numeral  or  sign  or  two  or  more 
of  each,  or  a  whole  word  or  group  of  figures,  com- 
bination of  conventional  signs,  or  combinations  of 
all  three  of  these  elements.  Thus  substitution 
ciphers  may  vary  from  those  of  extreme  simplicity 
to  those  whose  complication  defies  any  ordinary 
method  of  analysis  and  whose  solution  requires  the 
possession  of  long  messages  and  much  time  and 
study.  Fortunately  the  more  difficult  substitution 
ciphers  are  rarely  used  for  military  purposes,  on 
account  of  the  time  and  care  required  for  encipher- 
ing and  deciphering. 

Transposition  ciphers  are  limited  to  the  charac- 
ters of  the  original  text.  These  characters  are  re- 
arranged singly,  according  to  some  predetermined 
method  or  key  (monoliteral  transposition),  or  whole 
words  are  similarly  rearranged  (route  cipher) . 

There  may  also  be  a  combination  of  transposi- 
tion and  substitution  methods  in  enciphering  a  mes- 
sage but  in  this  case  it  will  fall  into  the  substitution 
class  on  first  determination  and  after  solution  as  a 
substitution  cipher  it  must  be  handled  as  a  trans- 
position cipher.  Examples  of  this  case  will  be  given. 
23 


—24— 

We  may  also  find  transposition  or  substitution 
methods  applied  to  words  taken  from  a  code  book, 
or  to  numbers  which  represent  these  words.  Thus 
cipher  methods  blend  into  code  work,  for  a  code  is, 
after  all,  only  a  specialized  substitution  cipher. 

We  can  now  lay  down  the  rules  for  determining 
whether  any  given  cipher  belongs  to  the  substitution 
class  or  to  the  transposition  class. 

Count  the  number  of  letters  in  the  message,  the 
number  of  vowels,  AEIOU,  the  number  of  the 
consonants,  LNRST,  and  the  number  of  the  con- 
sonants, JKQXZ. 

If  the  text  is  English  and  the  cipher  is  a  trans- 
position cipher,  this  proportion  will  hold;  vowels 
AEIOU  constitute  40%  of  the  whole;  consonants 
LNRST,  30%  and  consonants  JKQXZ,  3%. 

If  the  text  be  Spanish  the  proportions  for  a 
transposition  cipher  will  be:  vowels  AEIOU  45%, 
consonants  LNRST,  30%;  consonants  JKQXZ,  2%. 

If  these  proportions  do  not  hold  within  5%,  one 
way  or  the  other,  the  cipher  is  certainly  a  substitu- 
tion cipher.  Note,  however,  that  often  the  end  of  a 
message  is  filled  with  letters  like  K,  X,  Z  to  complete 
cipher  words  and  it  is  best  to  neglect  the  last  word  or 
words  in  making  a  count.  Also,  if  the  cipher  be  a 
long  one,  this  determination  can  safely  be  made  by 
taking  100  or  200  consecutive  letters  of  the  message, 
either  from  the  beginning  or,  if  nulls  at  the  begin- 
ning are  suspected,  from  the  interior  of  the  message. 

The  distinction  between  the  route  cipher  (trans- 
position) and  the  substitution  cipher  where  whole 
words  are  substituted  for  letters  of  the  original  text, 
must  be  made  on  the  basis  of  the  words  actually 
used.  It  is  better  to  consider  such  a  message  as  a 
route  cipher  when  the  words  used  appear  to  have 
some  consecutive  meaning  bearing  on  the  situation 


—25— 

at  hand.  A  substitution  cipher  of  this  variety  would 
only  be  used  for  transmission  of  a  short  message  of 
great  importance  and  secrecy,  and  then  the  chances 
are  that  certain  words  corresponding  to  A,  E,  N,  0 
and  T  would  appear  with  such  frequency  as  to  point 
at  once  to  the  fact  that  a  substitution  cipher  was 
used.  Watch  the  initial  or  terminal  letters  in  such 
a  cipher ;  they  may  spell  the  message. 

In  general,  the  determination  of  class  by  pro- 
portion of  vowels,  common  consonants  and  rare  con- 
sonants may  be  safely  followed.  We  will  now  pro- 
ceed to  the  examination  of  the  more  common  va- 
rieties of  each  class  of  cipher. 


Chapter  V 

Examination  of  Transposition  Ciphers 

gFTER  having  decided  that  a  cipher  belongs  to 
the  transposition  class,  it  remains  to  decide  on 
the  variety  of  cipher  used.     As,  by  definition, 
a  transposition  cipher  consists  wholly  of  characters 
of  the  original  message,  rearranged  according  to 
some  law,  we  may,  in  general,  say  that  such  a  cipher 
offers  fewer  difficulties  in  solution  than  a  substitu- 
tion cipher.     A  transposition  cipher  is  like  a  picture 
puzzle ;  the  parts  are  all  there  and  the  solution  mere- 
ly involves  their  correct  arrangement. 

CASE  1. — Geometrical  ciphers.  This  case  in- 
cludes all  ciphers  in  which  a  certain  number  of  the 
characters  are  chosen  so  that  they  will  form  a 
square  or  rectangle  of  predetermined  dimensions; 
and  then  these  characters  are  arranged  according 
to  a  geometrical  design. 

Taking  the  message : 

ABCDEFGHIJKLMNOPQRSTUVWX 
of  twenty-four  letters  and  assuming  a  rectangle  of 
six  letters  horizontally,  and  four  letters  vertically, 
we  may  have : 

(a)  Simple  Horizontal: 

ABCDEF  FEDCBA  STUVWX  XWVUTS 

GHIJKL  LKJIHG  MNOPQR  RQPONM 

MNOPQR  RQPONM  GHIJKL  LKJIHG 

STUVWX  XWVUTS  ABCDEF  FEDCBA 

(b)  Simple  Vertical: 

AEIMQU  DHLPTX  UQMIEA  XTPLHD 

BFJNRV  CGKOSW  VRNJFB  WSOKGC 

CGKOSW  BFJNRV  WSOKGC  VRNJFB 

DHLPTX  AEIMQU  XTPLHD  UQMIEA 

26 


(c)     Alternate  Horizontal: 


ABCDEF  FEDCBA  XWVUTS  STUVWX 

LKJIHG  GHIJKL  MNOPQR  RQPONM 

MNOPQR  RQPONM  LKJIHG  GHIJKL 

XWVUTS  STUVWX  ABCDEF  FEDCBA 


(b)     Alternate  Vertical: 


AHIPQX  DELMTU  XQPIHA  UTMLED 

BGJORW  CFKNSV  WROJGB  VSNKFC 

CFKNSV  BGJORW  VSNKFC  WROJGB 

DELMTU  AHIPQX  UTMLED  XQPIHA 


(e)     Simple  Diagonal: 


ABDGKO  GKOSVX  OKGDBA  XVSOKG 

CEHLPS  DHLPTW  SPLHEC  WTPLHD 

FIMQTV  BEIMQU  VTQMIF  UQMIEB 

JNRUWX  ACFJNR  XWURNJ  RNJFCA 

ACFJNR  JNRUWX  RNJFCA  XWURNJ 

BEIMQU  FIMQTV  UQMIEB  VTQMIF 

DHLPTW  CEHLPS  WTPLHD  SPLHEC 

GKOSVX  ABDGKO  XVSOKG  OKGDBA 


(/)     Alternate  Diagonal : 


ABFGNO  GNOUVX  ONGFBA  XVUONG 

CEHMPU  FHMPTW  UPMHEC  WTPMHF 

DILQTV  BEILQS  VTQLID  SQLIEB 

JKRSWX  ACDJKR  XWSRKJ  RKJDCA 

ACDJKR  JKRSWX  RKJDCA  XWSRKJ 

BEILQS  DILQTV  SQLIEB  VTQLID 

FHMPTW  CEHMPU  WTPMHF  UPMHEC 

GNOUVX  ABFGNO  XVUONG  ONGFBA 


(g)     Spiral,  clockwise: 


ABCDEF  LMNOPA  IJKLMN  DEFGHI 

PQRSTG  KVWXQB  HUVWXO  CRSTUJ 

OXWVUH  JUTSRC  GTSRQP  BQXWVK 

NMLKJI  IHGFED  FEDCBA  APONML 

(h)     Spiral,  counter  clockwise: 

APONML  NMLKJI  IHGFED  FEDCBA 

BQXWVK  OXWVUH  JUTSRC  GTSRQP 

CRSTUJ  PQRSTG  KVWXQB  HUVWXO 

DEFGHI  ABCDEF  LMNOPA  IJKLMN 

It  is  simply  a  matter  of  inspection  to  read  a  mes- 
sage in  a  cipher  of  this  type,  once  the  dimensions  of 
the  rectangles  have  been  determined.  We  place  the 
whole  or  a  portion  of  the  message  in  such  rectangles 
and  read  horizontally,  vertically  and  diagonally  for- 
ward and  backward.  Parts  of  words  will  at  once 
be  apparent  and  the  whole  message  is  soon  decipher- 
ed. Two  examples  will  show  the  process. 


—28— 
Message 

ILVGIOIAEITSRNMANHMNG 
This  message  contains  eight  vowels  or  38%  out 
of  twenty-one  letters,  and  the  letters  LNRST  occur 
7  times  or  33%,  the  letters  XQJKZ  not  appearing. 
It  is  therefore  a  transposition  cipher.  Twenty-one 
letters  immediately  suggest  seven  columns  of  three 
letters  each  or  three  columns  of  seven  letters  each. 
Trying  the  former  we  have : 

I  L  V  G  I  O  I 
A  E  I  T  S  R  N 
M  A  N  H  M  N  G 

and  reading  down  each  column  in  succession  (Case 
1-b)  reveals  the  message  to  be  "I  am  leaving  this 
morning." 

Message 

MSIBR  ORSEEVUEEM  CORER  ELIDE  TOEPQ 

ENRER  NSERY  ECOLL  EREUS  PLURC  ELOAJ 

AEHUH  PFASO  NNOAA  EPIUA  PPEAC  UQARU 

OPOEI  IRRMI  AFDAA  RQUBO  ZAEGE  RSFSX 

There  are  120  letters  in  this  message  with  57 
vowels  or  47%  vowels,  and  the  letters  LNRST  oc- 
cur 31  times  or  26%  of  the  whole. 

Non-occurrence  of  K  and  W  and  vowel  propor- 
tion leads  us  to  the  assumption  that  it  is  a  transpo- 
sition cipher  of  a  Spanish  text.  The  factors  of  120 
are  5x3x2x2x2.  We  may  then  have  one  rect- 
angle of  4  x  30  or  one  of  5  x  24  or  two  of  5  x  12,  or 
three  of  5  x  8,  or  four  of  5  x  6,  of  five  of  3  x  8,  or  ten 
of  3  x  4,  or  twenty  of  3  x  2.  The  message  being  in  a 
rectangle  of  4  x  30,  we  can  inspect  it  as  it  stands  and 
this  is  clearly  not  the  arrangement  if  it  be  a  geomet- 
rical transposition  cipher  at  all.  It  is  best  however 
to  try  the  largest  possible  rectangles  first  so  we  will 
put  it  in  the  form  5  x  24,  thus : 

MSIBRORSEEVTJEEMCORERELID 
E  TOEPQENRERNSERYECOLLERE 
U  SPLURCELO  A  JAEHUHPPASONN 
OAAEPIUAPPEACUQARUOPOEI  I 
RRMIAFDAAR  QUBOZAEGERSFSX 


—29— 

Here  an  inspection  shows  this  to  be  Case  1-f, 
alternate  diagonal,  and  the  text  to  be  "ME  SITUO 
SOBRE  PARRAL  PORQUE  ME  PRESENCIA  FUE 
REVELADA  POR  U";  here  the  sense  breaks  but 
note  that  U  is  the  twelfth  letter  of  the  line  and  con- 
tinue as  if  the  rectangle  were  5  x  12  and  we  have 
"NA  PAREJA  QU."  Now  inspect  the  second  rect- 
angle of  5  x  12  in  the  same  way  and  the  sense  con- 
tinues "E  SE  ME  ACERCO  Y  HUBO  QUE  RE- 
CHAZAR  POR  EL  FUEGO  ALLI  ESRERO  OR- 
DENES  FINISX". 

The  practical  way  of  examining  a  cipher  of 
this  type  is  to  have  several  men  prepare  rectangles 
of  different  dimensions,  using  the  letters  of  the  ci- 
pher in  the  order  received.  The  rectangles  can  be 
inspected  very  rapidly  when  once  prepared.  Note 
that  the  dimensions  of  any  rectangle  will  rarely  be 
such  as  to  contain  more  than  fifty  letters,  on  account 
of  the  necessity  of  filling  up  a  rectangle  with  nulls 
if  the  number  of  letters  of  the  message  is  just  a  little 
greater  than  a  multiple  of  the  rectangle.  Also  large 
rectangles  give,  for  all  but  the  diagonal  method, 
whole  words  in  a  line  or  column  and  these  are  easily 
noted. 

The  following  ciphers  come  under  Case  1 : 
CASE  1-i. — The  rail  fence  cipher,  useful  as  an 
operators'  cipher  but  permits  of  no  variation  and  is 
therefore  read  almost  as  easily  as  straight  text  when 
the  method  is  known.     The  message : 

HOSTILE  CAVALRY  HAS  RETIRED 

is  written: 

OTLCVLYARTRD 
HSIEAARHSEIE 

and  is  sent  : 

OTLCV  LYART  RDHSI  EAARH  SEIEX 


—30— 

CASE  1-j. 

Message 

SSOHS  TPFOR  IEEAE 
TQNET  FAIXE  GLFDR 
AULRN  OSRXL  HATRO 

To  solve  this  cipher,  read  down  the  columns  in 
this  order  8,  1,  15,  2,  14,  3,  13,  4,  12,  etc.  A  varia- 
tion is  to  arrange  the  cipher  so  the  columns  are  read 
upwards.  Another  is  to  arrange  the  ciphers  so  the 
columns  are  read  alternately  upward  and  downward. 
The  factors  of  the  number  of  letters  in  this  case  give 
the  shape  of  the  rectangle  as  usual. 

It  will  be  seen  that  there  are  a  great  number  of 
possible  transposition  ciphers  that  come  under  Case 
1  but  practically  all  of  them  are  useless  from  a  mil- 
itary standpoint  because  they  do  not  depend  on  a 
key  which  can  be  readily  and  frequently  changed. 
However  such  ciphers  constantly  crop  up  in  cipher 
examination,  being  used  for  special  communication 
between  parties  who  consider  the  regular  military 
ciphers  too  complicated.  Thus  some  of  these  expedi- 
ents have  been  used. 

REVERSED  WRITING. —  (Special  case  of  Case  1-a) . 

LEAVING  TONIGHT  is  enciphered  THGINOT 
GNIVAEL  or  it  may  be  reversed  by  words,  thus 
GNIVAEL  THGINOT  or  by  groups  of  five  letters, 
thus  IVAEL  NOTGN  XTHGI. 

VERTICAL  WRITING. —  (Special  case  of  Case  I-b) . 
Same  message  is  enciphered, 
LT 
EO 
AN 

VI  and  is  sent,  LTEOA  NVIIG  NHGTX. 

IG 
NH 
GT 


—31— 

CASE  2. — This  case  includes  all  transposition 
ciphers  in  which  lines  and  columns  of  the  text  are 
rearranged  according  to  some  key  word  or  key  num- 
ber. There  are  many  varieties  of  this  case  but  their 
solution  usually  is  arrived  at  through  the  methods 
suggested  for  Case  1,  that  is,  arrangement  into 
appropriate  rectangles  and  examination  of  lines  and 
columns  for  words  or  syllables.  Rearrangement  of 
columns  or  lines  follows  until  the  solution  is  com- 
pleted. 

CASE  2-a.  Message 

HIIGF       TNGHI      NTCVN    IEIOT       CYIFY     LHAEA  ESNBA    EEEEN 
RWGBN   YDELR     OAESG    RNEBO    VNLDA  ICAOA     LCNDT    IRGVA 
CDOIE      SEREC      DVPEI     AFIFL      RINEH    ETT 

There  are  108  letters  in  this  message  and  ex- 
amination shows  it  to  be  a  transposition  cipher, 
English  text.  The  number  of  letters,  108,  immedi- 
ately suggests  a  rectangle  of  12  x  9  or  9  x  12  letters. 
Put  into  this  form  we  have : 

Vowels  Vowels 

HIIGFTNGHINT         3  HIIGFTNGH  2 

CVNIEIOTCYIF         5  INTCVNIEI  4 

YLHAEAESNBAE         6  OTCYIFYLH  2 

EEENRWGBNYDE         4  AEAESNBAE  6 

LROAESGRNEBO         5  EEENRWGBN  3 

VNLDAICAOALC         5  YDELROAES  4 

NDTIRGVACDOI         4  GRNEBOVNL  2 

ESERECDVPEIA         6  DAICAOALC  5 

FIFLRINEHETT         4  NDTIRGVAC  2 

DOIESEREC  5 

DVPEIAFIF  4 

LRINEHETT  3 

The  vowel  count  of  the  lines  shows  the  first 
arrangement  to  be  the  more  likely.  We  will  now 
number  the  columns  and  try  pairing  off  certain  ones 
which  in  no  line  would  give  impossible  combinations 
of  letters. 

1   234567   89  10  11  12 
HIIGFTNGHINT 

CVNIEIOTC  Y  I  F 

YLHAEAESN  B  A  E 

EEENRWGBN  Y  D  E 

LROAESGRN  E  B  O 

VNLDAICAO  A  L  C 

NDTIRGVAC  D  O  I 

ESERECDVP  E  I  A 

FIFLRINEH  E  T  T 


—32— 

These  combinations  appear  among  others 


1 

6 

2 

4 

5 

2 

H 

T 

I 

G 

F 

I 

C 

I 

V 

I 

E 

V 

Y 

A 

L 

A 

E 

L 

E 

W 

E 

N 

R 

E 

L 

S 

R 

A 

E 

R 

V 

I 

N 

D 

A 

N 

N 

G 

D 

I 

R 

D 

E 

C 

S 

R 

E 

S 

F 

I 

I 

L 

R 

I 

The  word  FIGHT  stares  at  us  from  the  first 
line ;  let  us  arrange  the  columns  thus : 


5 
F 
E 
E 
R 
E 
A 
R 
E 
R 

2 
I 
V 
L 
E 
R 
N 
D 
S 
I 

4 
G 
I 
A 

N 
A 
D 
I 
R 
L 

1 
H 
C 
Y 

E 
L 

V 
N 
E 
F 

6 
T 
I 
A 
W 
S 
I 
G 
C 
I 

3 
I 
N 
H 
E 
O 
L 
T 
E 
F 

We  have  the  words  FIGHTI(NG),  VICIN- 
(ITY),  RENEWE(D),  ANDVIL(LA),  RDINGT- 
(0),  RECE(IVED).  With  this  to  go  on,  we  must 
choose  column  11  as  the  next  one  and  then  in  order, 
columns  8,  10,  7,  12,  9.  But  note  that  the  order  11, 
8,  10,  7,  12,  9,  is  the  same  as  the  order  5,  2,  4,  1,  6,  3. 
The  message  was  written  in  twelve  columns  and  the 
columns  have  been  transposed  in  that  order.  We 
may,  although  it  is  entirely  unnecessary,  speculate 
on  the  key  word  used.  It  was  probably 

MEXICO 
4      26315 

meaning  that  the  4th  column  of  the  plain  text  was 
transferred  in  enciphering  so  it  became  our  1st,  the 
2d  column  remained  the  2d ;  the  6th  column  became 
our  3d,  etc. 

Actually,  this  cipher  was  solved  because  the 
word  VILLA  was  suspected  and  all  the  necessary 
letters  were  found  in  line  six  of  the  arrangement  in 


—33— 

twelve  columns.     The  order  1,  6,  3,  11,  8  was  tried 
and  gave  this  result. 

l  6  3  11  8 

H  T  I  N  G 

C  I  N  I  T 

Y  A  H  A  S 

E  W  E  D  B 

L  S  0  B  R 
VILLA 

N  G  T  0  A 

E  C  E  I  V 

F  I  F  T  E 

The  remainder  of  the  solution  followed  the  lines 
already  laid  down  and,  naturally,  offered  no  difficul- 
ties, in  view  of  the  large  number  of  connected  sylla- 
bles available. 

CASE  2-b. 

Message 

SLCOF  WEETN  EBRDO  ORVYM  FFEDI 

NMTEC  ROIAR  PERHO  ESETS  RFBHL 

TENAH  OPTAU  SOMTL  RTETT  ASCBH 

NIODC  RENEN  AAPRD  LACYE  ECIIE 
S  G  U  F  N 

This  is  a  transposition  cipher,  English  text,  and 
contains  105  letters.  The  factors  of  105  are  5  x  3  x 
7  so  that  we  must  investigate  the  following  rect- 
angles; 5  x  21,  15  x  7,  three  of  5  x  7,  five  of  3  x  7 
and  seven  of  5  x  3. 

21x5  Vowels       5x21     Vowels 

SLCOFWEETNEBRDOORVYMF  6  SLCOF  1 

FEDINMTECROIARPERHOE     S  9  WEETN  2 

ETSRFBHLTENAHOPTAUSOM  7  EBRDO  2 

TLRTETTASCBHNIODCRENE  6  ORVYM  1 

NAAPRDLACYEECIIE8GUFN  9  FFEDI  2 

Vowels  121210140133133311321          NMTEC       1 

ROIAR         3 

The  vowel  count  of  the  columns  £  s  E  ?  s  I 

of  the  rectangle  5  x  21  is  very  satis-  ?  ^  N  J  H  2 

factory.     Let  us  consider  it  as  three  °  o  M  "T  L  i 

blocks  of  5  x  7  each,  since  we  must  «  £  ®  *  *  J 

do  this  ultimately,  and  make  a  vowel  £  EJ  °  £  £  | 

count  of  columns  for  these  blocks.  TA  A  jf  «  D  | 

LACYE  £ 
ECIIE  4 
S  G  U  F  N  1 

Vowels      79876 


—34— 

Column 
12345 

Vowels,  1st  block  22322 
Vowels,  2d  block  23222 
Vowels,  3d  block  -  34322 

This  is  also  excellent,  so  we  will  try  three  blocks 
5x7  and  see  if  rearrangement  of  horizontal  lines 
will  give  results  reading  the  columns  vertically. 

1  SLCOF  PERHO  ASCBH 

2  WEETN  ESETS  NIODC 

3  EBRDO  RFBHL  RENEN 

4  ORVYM  TENAH  AAPRD 

5  FFEDI  OPTAU  LACYE 

6  NMTEC  SOMTL  ECIIE 

7  ROIAR  RTETT  SGUFN 

Among  other  combinations  are : 

3  EBRDO  RFBHL  RENEN 
2  WEETN  ESETS  NIODC 
1  SLCOF  PERHO  ASCBH 

5  FFEDI  OPTAU  LACYE 
7  ROIAR  RTETT  SGUFN 

The  addition  of  line  6  above  line  3  and  line  4  be- 
low line  7  will  complete  this  cipher.  The  successive 
columns  should  be  read  downward. 

CASE  2-c.  In  this  case,  both  lines  and  columns 
are  rearranged  by  means  of  a  key  word  or  key  words. 
The  method  of  solution  is  the  same  as  Case  2-a  and 
2-b  except  that  the  lines  must  be  rearranged  after 
the  columns  have  been  correctly  arranged,  or  in  some 
cases,  vice  versa.  This  cipher  is  not  infrequently 
met  with  because  it  seems  to  offer  safety  by  use  of 
two  key  words  and  by  the  great  but  only  apparent 
complexity  of  the  method. 


Message 

T  F  T  o  r 
G  x  i  x  > 

U  D  N  N  E 

This  is  a  transposition  cipher,  English  text  and 


WVGAE  EGENL  TFTOH  TEIEF  RBTSE 
INENG  ONWRM  GXIXN  GOITN  ROMRO 
ESPAL  HNEAC  UDNNH  DERME 


the  number  of  letters,  70,  leads  us  to  try  rectangles 
of  10  x  7  and  7  x  10. 

Vowels  Vowels 

WVGAEEGENL      4    WVGAEEG  3 

TFTOHTEIEF      3    ENLTFTO  2 

RBTSEINENG      3    HTEIEFR  3 

ONWRMGXIXN     2    BTSEINE  3 

GOITNROMRO     4    NGONWRM  1 

ESPALHNEAC     4    GXIXNGO  2 

UDNNHDERME     3    ITNROMR  2 

OESPALH  3 

NEACUDN  3 

NHDERME  2 

The  first  form  looks  the  more  likely  from  the 
vowel  count.  We  proceed  to  number  the  columns 
and  lines  and  try  rearrangement  of  columns  so 
as  to  obtain  possible  letter  combinations  from  every 
line. 

123456789    10 

1  WVGAEEGEN  L 

2  TFTOHTEIEF 

3  RBTSEINENG 

4  ONWRMGXIXN 

5  GOITNROMRO 

6  E    S   P  AL  HN  E  A    C 

7  UDNNHDERME 

Among  other  combinations  we  have  these : 


1 

2 
3 
4 
5 

6 
7 

3  5 
G  E 
T   H 
T   E 
WM 
I    N 
P  L 
N  H 

1  4 
W  A 
T   O 
R  S 
0  R 
G  T 
E  A 
U  N 

2  8 
V  E 
F   I 
B   E 
N  I 
O  M 
S   E 
D  R 

10  6 
L  E 
F   T 
G    I 
N   G 
O   R 
C   H 
E  D 

9  7 
N  G 
E   E 
N   N 
X  X 
R  O 
A  N 
M  E 

A  very  casual  inspection  of  the  lines  shows  that 
they  should  be  rearranged  in  order  6,  1,  2,  7,  3,  5, 
4,  as  follows: 


351428  10  697 

6  PLEASE  CHAN 

1  G  EW AVE  L  E  NG 

2  THTOFIFTEE 

7  NH  UNDRE  D  M  E 

3  TERSBEG  I  NN 
5  I  N  GTOM  O  R  RO 
4W MORNING  XX 


Although  of  no  particular  importance,  it  may  be 
stated  that  the  column  key  in  this  case  was  GRAND 


—36— 

and  the  line  key  was  CENTRAL,  both  used  as  in 
enciphering  Case  2-a. 

CASE  3.  Route  ciphers.  In  this  case,  whole 
words  of  the  message  are  transposed  according  to 
some  of  the  methods  of  Case  1  or  2  or  their  equiva- 
lents. The  route  cipher  is  little  used  at  present. 
Its  development  and  use  during  the  Civil  War 
was  caused  by  the  inability  of  the  telegraphers 
of  that  day  to  handle  regular  cipher  matter  correctly 
and  rapidly.  It  was,  even  in  those  days,  frankly 
only  a  delaying  cipher  and,  to  be  of  any  value,  had 
to  be  filled  with  meaningless  words  to  conceal  the 
message  proper.  An  example  from  the  Signal 
Book  will  suffice  to  show  the  general  character  of 
route  ciphers.  To  one  familiar  with  monoliteral 
transposition  ciphers,  even  the  best  of  route  ciphers 
offers  but  little  difficulty. 

"To  encipher  the  message  'MOVE  DAYLIGHT. 
ENEMY  APPROACHING  FROM  NORTH.  PRI- 
SONERS SAY  STRENGTH  ONE  HUNDRED 
THOUSAND.  MEET  HIM  AS  PLANNED/  ar- 
range as  follows : 

MOVE  STRENGTH  PLANNED  SAY 

DAYLIGHT  ONE  AS  PRISONERS 

ENEMY  HUNDRED  HIM  NORTH 

APPROACHING  THOUSAND  MEET  FROM 

Here  the  route  is  down  the  first  column,  up  the 
fourth,  down  the  second  and  up  the  third." 

This  cipher  was  often  complicated  by  the  intro- 
duction of  nulls  for  every  fifth  word.  Thus  the 
above  message  might  be  sent: 

MOVE  STRENGTH  PLANNED  SAY  NEVER 
DAYLIGHT  ONE  AS  PRISONERS  LEAVING 
ENEMY  HUNDRED  HIM  NORTH  UNCHANGED 
APPROACHING  THOUSAND  MEET  FROM 
COME. 

The  words  in  italics  are  nulls  and  not  a  part  of 


—37— 

the  message  and  the  receiver  eliminates  them  before 
arranging  his  message  in  columns  to  get  the  sense 
of  it. 

As  an  additional  complication,  it  was  customary 
for  each  correspondent  to  have  a  dictionary  or  code 
in  which  the  names  of  all  prominent  generals  and 
places  and  many  of  the  prominent  verbs,  — as  to 
march,  to  sail,  to  encamp,  to  attack,  to  retreat, 
— were  represented  by  other  words. 

A  route  cipher  using  the  code  words  of  the  War 
Department  code  might  have  some  advantages  over 
the  method  of  enciphering  code  messages  as  pre- 
scribed in  that  Code. 

General  Remarks  on  Transposition  Ciphers 

It  is  the  consensus  of  opinion  of  experts  that  tht 
transposition  cipher  is  not  the  best  one  for  military 
purposes.  It  does  not  fulfill  the  first,  second,  and 
third  of  KirckhofFs  requirements  as  to  indecipher- 
ability,  safety  when  apparatus  and  method  fall  into 
the  hands  of  the  enemy,  and  dependability  on  a  readi- 
ly changeable  key  word. 

However,  transposition  ciphers  are  often  en- 
countered. They  are  favorites  with  those  who  find 
the  substitution  ciphers  too  difficult  and  too  tedious 
to  handle  and  who  believe  that  their  transposition 
methods  are  either  absolutely  indecipherable  or  suffi- 
ciently so  for  the  purpose  of  concealing  the  text  of  a 
message  for  the  time  being.  They  seem  to  be  par- 
ticularly popular  with  secret  agents  and  spies,  pre- 
sumably because  special  apparatus  is  rarely  neces- 
sary in  enciphering  and  deciphering. 

Although  the  number  of  transposition  methods 
is  legion,  they  can  practically  all  be  considered  un- 
der one  of  the  three  cases  already  discussed.  It  is 
surprising  how  often  transposition  ciphers  prepared 


—38— 

by  complicated  rules,  will,  on  analysis,  be  seen  to  be 
very  simple. 

To  be  successful  in  solving  transposition  ciphers, 
one  should  constantly  practice  reading  backward  and 
up  and  down  columns,  so  that  the  common  combina- 
tions of  letters  are  as  quickly  identified  when  seen 
thus  as  when  encountered  in  straight  text.  Combi- 
nations like  EHT,  LLIW,  ROF,  DNA,  etc.,  should  be 
appreciated  immediately  as  common  words  written 
backward. 

A  study  of  the  table  of  frequency  of  digraphs  or 
pairs  is  also  excellent  practice  and  such  a  table  should 
be  at  hand  when  a  transposition  cipher  is  under  con- 
sideration. It  assists  greatly  if  Case  2  be  encoun- 
tered and  is  of  considerable  use  in  solving  Case  1. 

The  solution  of  route  ciphers  is  necessarily  one 
of  try  and  fit,  with  the  knowledge  that  such  ciphers 
usually  are  read  up  and  down  columns.  It  is  not 
believed  that  route  ciphers  will  often  be  met  with  at 
the  present  day. 


Chapter  VI 


Examination  of  Substitution  Ciphers 

HEN  an  unknown  cipher  has  been  put  into  the 
substitution  class  by  the  methods  already  de- 
scribed we  may  proceed  to  decide  on  the  vari- 
ety of  substitution  cipher  which  has  been  used. 

There  are  a  few  purely  mechanical  ways  of  solv- 
ing some  of  the  simple  cases  of  substitution  ciphers 
but  as  a  general  rule  some  or  all  of  the  following  de- 
terminations must  be  made : 

1.  By  preparation  of  a  frequency  table  for  the 
message  we  determine  whether  one  or  more  substi- 
tution alphabets  have  been  used  and,  if  one  only  has 
been  used,  this  table  leads  to  the  solution. 

2.  By  certain  rules  we  determine  how  many 
alphabets  have  been  used,  if  there  are  more  than  one, 
and  then  isolate  and  analyze  each  alphabet  by  means 
of  a  frequency  table. 

3.  If  the  two  preceding  steps  give  no  results 
we  have  to  deal  with  a  cipher  with  a  running  key,  a 
cipher  of  the  Playfair  type,  or  a  cipher  where  two 
or  more  characters  are  substituted  for  each  letter  of 
the  text.     Some  special  cases  under  this  third  head 
will  be  given  but,  in  general,  military  ciphers  of  the 
substitution  class  will  usually  be  found  to  come  un- 
der the  first  two  heads,  on  account  of  the  time  and 
care  required  in  the  preparation  and  deciphering  of 
messages  by  the  last  named  methods  and  the  neces- 
sity, in  many  cases,  of  using  complicated  machines 
for  these  processes. 

39 


CASE  4-a. 

Message 

OBQFO    BPBRP    QBAML    OBHIF    PILFQ    FJBOX    OFLNR    BIXOZ    EL 

From  the  recurrence  of  B,  F  and  O,  we  may 
conclude  that  a  single  substitution  alphabet  was  used 
for  this  message.  If  so  and  if  the  alphabet  runs  in 
the  same  order  and  direction  as  the  regular  alphabet, 
the  simplest  way  to  discover  the  meaning  of  the  mes- 
sage is  to  take  the  first  two  words  and  write  alpha- 
bets under  each  letter  as  follows,  until  some  line 
makes  sense : 

OBQFOBPBRP 

PCRGPCQCSQ 

QDSHQDRDTR 

RETIRESEUS 

The  word  RETIRESE  occurs  in  the  fourth  line, 
and,  if  the  whole  message  be  handled  in  this  way  we 
find  the  rest  of  the  fourth  line  to  read  USTED  FOR 
EL  MISMO  ITINERARIO  QUE  MARCHO.  The 
message  was  enciphered  using  an  alphabet  where 
A=X,  B=Y,  C=Z,  D=A,  etc.  noting  that  as  this 
message  is  in  Spanish  the  letters  K  and  W  do  not 
appear  in  the  alphabet. 


—41— 

CASE  4-b. 

Message 

HUJZH  UIUPN  OZYTS   VQXMI   SMOMX  MQHUD  UMREI   SESJU   AG 

This  is  a  message  in  Spanish.  We  will  handle 
it  as  in  case  4-a,  setting  down  the  whole  message. 

HU  JZHU I  UPNOZ  YT  SVQXMISMOMXMQHUDUMR  EISESJUAG 
IVL  AIVJVQOPAZUTXRY    A=A    NYNR I VEVNSF J TFTLVB H 

J  X  MB  J  XLXR  PQB A VUYSZ  O  Z  O  S  J  XFXO  TGL  UGUMX  O  I 

LY  NCL  YM YSQRCBXVZTA  P  A  P  T  L  YGY  PUHMVH VNYD  J 

MZODMZNZTRSDCYXAUB  QBQUMZHZQVI  NXIXOZE  L 

NAPE NAOAUSTEDZ YB V G  RCRVN  A  IARXJO  YJ  Y  PAFM 

OBQFOBPB    A=U    AZCXD  S  D  SXO  B  JBS  YLP  Z  L  Z  QBGN 

PCRGP  CQC  BAD  YE  T  E  T  YP  C  LOT  ZMQAMAR  CHO 

QDSHQDRD  CBEZF  UF  UZ  QDMDUANRB        A=S 

RETIRESE  DCFAG  VGVARENEVB O SC 

A=Q  EDGBH  XHXBSFOFXCPTD 

FEHC  I  Y  I YC  T  G  PGYD  QUE 

GFIDJ  Z JZDUHQHZE  A=0 

HGJEL^  ALAEVIRIAF 

IHLA=M  BMBFXJSJBG 

JIM  CNCGYLTLCH 

LJN  DODHZMUMDI 

MLO  EPEIANVNEJ 

NMP  FQFJBOXOFL 

ONQ  G  R  GLC  P  YPGM 

POR  HSHMDQZQHN 

A=E  I  T I NERARIO 
A=D 

Here  each  word  of  the  message  comes  out  on  a 
different  line,  and  noting  in  each  case  the  letter  cor- 
responding to  A,  we  have  the  word  QUEMADOS 
which  is  the  key.  The  cipher  alphabet  changed  with 
each  word  of  the  message. 

A  variation  of  this  case  is  where  the  cipher  al- 
phabet changes  according  to  a  key  word  but  the 
change  comes  every  five  letters  or  every  ten  letters 
of  the  message  instead  of  every  word.  The  text  of 
the  message  can  be  picked  up  in  this  case  with  a  lit- 
tle study. 

Note  in  using  case  4  that  if  we  are  deciphering 
a  Spanish  message  we  use  the  alphabet  without  K 
or  W  as  a  rule,  altho  if  the  letters  K  or  W  appear  in 


the  cipher  it  is  evidence  that  the  regular  English  al- 
phabet is  used. 

CASE  5-a. 

Message 

DNWLW       MXYQJ       ANRSA       RLPTE       CABCQ       RLNEC       LMIWL 
XZQTT        QIWRY        ZWNSM       BKNWR        YMAPL       ASDAN 

This  message  contains  K  and  W  and  therefore 
we  expect  the  English  alphabet  to  be  used.  The 
frequency  of  occurrence  of  A,  L,  N,  R  and  W  has 
lead  us  to  examine  it  under  case  4  but  without  re- 
sult. Let  us  set  down  the  first  two  words  and  de- 
cipher them  with  a  cipher  disk  set  A  to  A  and  then 
proceed  as  in  case  4. 

Cipher  message  DNWLWMXYQJ 

Deciphered  A  to  A  XNEPEODCKR 

B  YOPQFPKDLS 

C  ZPGRGQFEMT 

D  AQHSHRGFNU 

E  BRITISHGOV 

The  message  is  thus  found  to  be  enciphered  with 
a  cipher  disk  set  A  to  E  and  the  text  is  :  BRITISH 
GOVERNMENT    PLACED    CONTRACTS    WITH 
FOLLOWING  FIRMS  DURING  SEPTEMBER. 
CASE  5-b. 

Same  as  case  4-b  except  that  the  cipher  message 
must  be  deciphered  by  means  of  a  cipher  disk  set  A 
to  A  before  proceeding  to  make  up  the  columns  of  al- 
phabets. The  words  of  the  deciphered  message  will 
be  found  on  separate  lines,  the  lines  being  indicated 
as  a  rule  by  a  key  word  which  can  be  determined  as 
in  case  4-b. 

The  question  of  alphabetic  frequency  has  al- 
ready been  discussed  in  considering  the  mechanism 
of  language.  It  is  a  convenient  thing  to  put  the  fre- 
quency tables  in  a  graphic  form  and  to  use  a  similar 
graphic  form  in  comparing  unknown  alphabets  with 
the  standard  frequency  tables.  For  instance  the 
standard  Spanish  frequency  table  put  in  graphic 


—43— 

form  is  here  presented  in  order  to  compare  with  it 
the  frequency  table  for  the  message  discussed  in 
case  4-a. 

Standard  Spanish  frequency  table 


111111111111111111111111111   27 

11  2 

111111111  9 

1111111111  10 
1111111111111111111111111111  28 

II  2 

III  3 
11  2 
111111111111  12 

I  1 
1111111111  10 
111111  6 
111111111111  12 
1111111111111111  16 
11111  5 

II  2 
111111111111111  15 
11111111111111  14 
11111111  8 
1111111  7 
11  2 


Table 

for  Message 

Case  4-a 

A 

1 

1 

B 

1111111 

7 

C 

D 

E 

1 

1 

F 

11111 

5 

G 

H 

1 

1 

I 

111 

3 

J 

1 

1 

L 

111 

3 

M 

1 

.     1 

N 

1 

1 

0 

111111 

6 

P 

111 

3 

Q 

111 

3 

R 

11 

2 

S 

T 

U 

V 

X 

11 

2 

Y 

Z 

1 

1 

Our  first  assumption  might  be  that  B=A  and 
F=E  but  it  is  evident  at  once  that  in  that  case,  S, 
T,  U  and  V  (equal  to  R,  S,  T  and  U)  do  not  occur 
and  a  message  even  this  short  without  R,  S,  T  or  U 
is  practically  impossible.  By  trying  B=E  we  find 
that  the  two  tables  agree  in  a  general  way  very  well 
and  this  is  all  that  can  be  expected  with  such  a  short 
message.  The  longer  the  message  the  nearer  would 
its  frequency  table  agree  with  the  standard  table. 
Note  that  if  a  cipher  disk  has  been  used,  the  alphabet 
runs  the  other  way  and  we  must  count  upward  in 
working  with  a  graphic  table.  Note  also  that  if,  in 
a  fairly  long  message,  it  is  impossible  to  coordinate 
the  graphic  table,  reading  either  up  or  down,  with 
the  standard  table  and  yet  some  letters  occur  much 
more  frequently  than  others  and  some  do  not  occur 
at  all,  we  have  a  mixed  alphabet  to  deal  with.  The 
example  chosen  for  case  6-a  is  of  this  character.  An 
examination  of  the  frequency  table  given  under  that 
case  shows  that  it  bears  no  graphic  resemblance  to 


—44— 

the  standard  table.  However,  as  will  be  seen  in 
case  7-b,  the  preparation  of  graphic  tables  enables 
us  to  state  definitely  that  the  same  order  of  letters 
is  followed  in  each  of  a  number  of  mixed  alphabets. 

General  Remarks 

Any  substitution  cipher,  enciphered  by  a  single 
alphabet  composed  of  letters,  figures  or  conventional 
signs,  can  be  handled  by  the  methods  of  case  6. 
For  example,  the  messages  under  case  4-a  and  5-a 
are  easily  solved  by  these  methods.  But  note  that 
the  messages  under  case  4-b  and  5-b  cannot  so  be 
solved  because  several  alphabets  are  used.  We  will 
see  later  that  there  are  methods  of  segregating  the 
different  alphabets  in  some  cases  where  several  are 
used  and  then  each  of  the  alphabets  is  to  be  handled 
as  below. 

CASE  6-a. 

Message 

QDBYP  BXHYS  OXPCP  YSHCS  EDRBS  ZPTPB  BSCSB  PSHSZ  AJHCD  '  OSEXV 
HPODA  PBPSZ  BSVXY  XSHCD 

This  message  was  received  from  a  source  which 
makes  us  sure  it  is  in  Spanish.  The  occurrence  of 
B,  H,  P  and  S  has  tempted  us  to  try  the  first  two 
words  as  in  case  4  and  5  but  without  result.  We  now 
prepare  a  frequency  table,  noting  at  the  same  time 
the  preceeding  and  following  letter.  This  latter  pro- 
ceeding takes  little  longer  than  the  preparation  of  an 
ordinary  frequency  table  and  gives  most  valuable  in- 
formation. 


Frequency  Table 


A  II 

B  IIIIIIII 

c  urn 

D  mil 

E  II 

F 

G 

H  Him 
I 

J  I 

L 

M 

N 

O  III 

P  IIIIIIIII 

Q  I 

R  I 

S  IIIIIIIIIIII 

T  I 

U 

V  II 

x  inn 

Y  IIII 

Z  III 


Prefix 

2    ZD 

8    DPRPBSPZ 
5     PHSHH 
5     QECOC 
2    SS 


6    XSSJVS 
1    A 


3  SDP 

9  YXCZTB.HAB 

1 

1  D 


Suffix 

JP 

YXSBSPPS 

PSSDD 

BROA 

DX 


YCSCPC 
H 


XSD 

BCYTBSOBS 

D 

B 


12  YYCBBCPHOPBX  OHEZCBHZEZVH 
IP  P 


2  XS 

5  BOEVY 

4  BHPX 

3  SSS 


HX 

HPVYS 

PSSX 
PAB 


It  is  clear  from  an  examination  of  this  table  that 
we  have  to  deal  with  a  single  alphabet  but  one  in 
which  the  letters  do  not  occur  in  their  regular  order. 

We  may  assume  that  P  and  S  are  probably  A 
and  E,  both  on  account  of  the  frequency  with  which 
they  occur  and  the  variety  of  their  prefixes  and  suf- 
fixes. If  this  is  so,  then  B  and  H,  are  probably 
consonants  and  may  represent  R  and  N  respectively. 
D  and  X  are  then  vowels  by  the  same  method  of  an- 
alysis. Noting  that  HC  occurs  three  times  and 
taking  H  as  N  we  conclude  that  C  is  probably  T. 
Substitute  these  values  in  the  last  three  words  of 


—46— 

the  message  because  the  letters  assumed  occur  rather 
frequently  there. 

PBPSZBSVXYXSHCD 
I     •  I  I 

ARAE      RE  ENT 

O        O  O 

Now  Z  is  always  prefixed  by  S  and  may  be  L. 
Taking  X=I  and  D=0,  (they  are  certainly  vowels) , 
V=G  and  Y— M,  we  have 

ARA  EL  REGIMIENTO 

Substituting  these  values  in  the  rest  of  the  mes- 
sage we  have 

QDBYPBXHYSOXPCPYSHCSEDRBSZPTPB 
ORMARINME      IATAMENTE     O      RELA     AR 

BSCSB    PSHSZ    AJHCD     OSEXVHPODA 
RETER    AENEL  NTO        E       IGNA       O 

We  may  now  take  Q=F,  0=D,  E=S,  R=B, 
T=C,  A=P  and  J=U  and  the  message  is  complete. 
We  are  assisted  in  our  last  assumption  by  noting  that 
S=E  and  E=S,  etc.,  and  we  may  on  that  basis  re- 
construct the  entire  alphabet.  The  letters  in  paren- 
thesis do  not  occur  in  the  message  but  may  be  safely 
assumed  to  be  correct. 

Ordinary    ABODE  FGHI    JLMN  OPQRSTUVXYZ 
Oipher      PRTOS(Q)(V)N(X)(U)(Z)(Y)(H)DAFBECJG  I  ML 

It  is  always  well  to  attempt  the  reconstruction 
of  the  entire  alphabet  for  use  in  case  any  more  cipher 
messages  written  in  it  are  received. 


—47— 


CASE  6-b. 

Message 

Lt.  J.  B.  Smith,  Royal  Flying  Corps,  Calais, 
France. 

DACFT     RRBHA    MOOUE     AENOI    ZTIET 


ASMOS 
OMEAH 
TLNDA 
AE  IOH 
AYBIS 
HL  I  LL 
AMOOU 
NHOOQ 
I  HTSW 

EOHIE 
NILGO 
OFTEN 
ABRIS 
DFTEN 
TWSOU 
EAYOE 
OBBOR 
ENOHO 

YOCKF 
OSAHU 
INTWN 
ODACF 
EFAPH 
GDENO' 
QISUU 
TSLHO 
PAHIH 

NO  HOE 
OHOUE 
BAFOH 
TRREN 
OSMNI 
UTHOM 
OLEHA 
BAHEO 
ITUAS 

NOUTH 
APCHS 
GROHT 
OSTSM 
ZTIEA 
EAHBH 
DENOE 
UBHOB 
BIHTL 

Graham- White. 

The  address  and  signature  indicate  that  this 
message  is  in  English. 

There  are  250  letters  in  the  cipher;  the  vowels 
AEIOU  occur  109  times  or  43.6%,  the  letters  LNRST 
occur  62  times  or  24.8%,  and  the  letters  KQVXZ  oc- 
cur 5  times  or  2%.  The  proportion  in  the  case  of 
the  vowels  is  somewhat  too  large  and,  in  the  case  of 
the  letters  LRNST,  it  is  too  small.  It  is  then  ques- 
tionable whether  this  is  a  transposition  cipher  altho, 
at  first  glance  it  might  appear  to  be  one. 

On  examination  for  parts  of  possible  words  we 
are  at  once  struck  by  the  occurrence  at  irregular  in- 
tervals of  recurring  groups,  viz : 


DACFTRR 
DACFTEN 

DACFTRR 
FTEN 


ENO 

ENOUTHOMEAH 

ENO 

DENOUTHOMEAH 

DENO 

ENO 


BHAMOOUEA 
BHAMOOUEA 

IZTIE 
IZTIE 


This  is  a  strong  indication  that  the  cipher  is  a 
substitution  cipher,  so,  to  make  an  examination  a 
frequency  table  will  be  constructed. 

Frequency  Table 

A    BCDEFGH    I    JKLMNOPQRSTU  V  WX  Y  Z 
23  11  7  6  24  7  3  26  16  0  1  8  8  15  36  3  2  8  14  17  11   1   30    32 


—48— 

Superficially,  this  looks  like  a  normal  frequency 
table,  but  0  is  the  dominant  letter,  followed  by  H, 
E,  A,  T,  I,  N,  S,  in  the  order  named.  It  is  certainly 
Case  6  if  it  is  a  substitution  cipher  at  all. 

Let  us  see  what  can  be  done  by  assuming  0=E; 
the  triplet  ENO,  occurring  six  times  might  well  be 
THE  and  E=T  and  N  =  H.  A  glance  at  the  fre- 
quency table  shows  this  to  be  reasonable.  Now  sub- 
stitute these  letters  in  some  likely  groups.  FNOH- 
OENO  becomes  _HE  JETHE;  FTEN  becomes  _TH; 
ENOENHO  becomes  THETH_E;  ENOHO  becomes 
THE_E.  A  bit  of  study  will  show  that  F= W,  T  =  I 
and  H=R  and  the  frequency  table  bears  this  out  ex- 
cept that  H(=R)  seems  to  occur  too  frequently.  The 
recurring  groups  containing  DAC  (see  above)  occur 
in  such  a  way  that  we  may  be  sure  DAC  is  one  word, 
FTRR  is  another  and  FTEN(  =  WITH)  is  a  third. 
Now  FTRR  becomes  WI ,  which  can  only  be  com- 
pleted by  a  double  letter.  LL  fills  the  bill  and  we 
may  say  R=L.  As  DAC  starts  the  message  and  is 
followed  by  FTRR  (=WILL)  it  is  reasonable  to  try 
DAC— YOU.  Looking  up  DAC  in  the  frequency 
table  it  is  evident  that  we  strain  nothing  by  this  as- 
sumption. We  now  have: 

Letters  of  cipher     ONTAHECFD 
Letters  of  message  EHIORTUWY 

Now  take  the  group  ENOUTHOMEAH  which 
occurs  twice.  This  becomes  THE  _IRE  JOR  and  if 
we  substitute  U=D  and  M=C  we  have  THE  DIREC- 
TOR. Next  the  group  (FTRR)BHAMOOUEA  be- 
comes (WILL)  ROCEEDTO  and  the  context  gives 
word  with  missing  letter  as  PROCEED,  from  which 
B=P,  Next  the  group  (ENO)  IZTIETASMOSEOH- 
lEYOCK(FNOHO)  becomes  (THE)_I_TIO_CE_ - 
TER_T_EUJ WHERE)  and  the  group  (FTEN)EFA- 
PHOSMNIZTIEAHL  becomes  (WITH)TWO_RE_CH 


—49— 

_I_TOR_.  The  substitution  of  A  for  I,  V  for  Z,N 
for  S  and  F  for  P  makes  the  latter  group  read  (WITH 
TWO  FRENCH  AVIATORS  and  the  former  read 
(THE)AVIATION  CENTER  AT  EUJ WHERE). 

Now  the  word  YOCK  =  (_EU_)  is  the  name  of 
a  place,  evidently.  WE  find  another  group  contain- 
ing Y,  viz:  ENOSTSMAYBISD  which  becomes  THE- 
NINCO_PANY  so  that  evidently  we  should  substi- 
tute M  for  Y.  The  other  occurrence  of  Y  (  =  M)  is 
in  the  group  EAYOEQISU  which  becomes  TOMET  - 
AND.  A  reasonable  knowledge  of  geography  gives 
us  the  words  MEUX  and  METZ  so  that  X  should  be 
substituted  for  K  and  Z  for  Q. 

We  now  have  sufficient  letters  for  a  complete  de- 
ciphering of  the  message. 

Letters  of  cipher     ABCDEPGHIKLMNOPQRSTUVWYZ 
Letters  of  message  OPUYTW   RAXSCHEFZLNID MV 

The  message  deciphers: 

YOU  WILL  PROCEED  TO  THE  AVIATION  CENTER 
AT  MEUX  WHERE  THE  DIRECTOR  HAS  _EEN  OR- 
DERED TO  FURNISH  YOU  WITH  A  HI_H  POWER 
JLERIOT  AEROPLANE.  YOU  WILL  THEN  IN  COM- 
PANY WITH  TWO  FRENCH  AVIATORS  ASSI  NED  _Y 
THE  DIRECTOR  PROCEED  TO  METZ  AND  DESTROY 
THE  THREE  ZEPPELINS  REPORTED  PREPARIN_ 
THERE  FOR  A  RAID  ON  PARIS. 

The  substitution  of  B  for  G,  G  for  W  and  K  for 
V  completes  the  cipher.  This  cipher  is  difficult  only 
because  the  cipher  alphabet  is  made  up,  not  hap- 
hazard, but  scientifically  with  proper  consideration 
for  the  natural  frequency  of  occurrence  of  the  let- 
ters. In  cipher  work  it  is  dangerous  to  neglect  proper 
analysis  and  jump  at  conclusions. 

In  the  study  of  Mexican  substitution  ciphers, 
several  alphabets  have  been  found  which  are  made 
up  in  a  general  way,  like  the  one  discussed  in  this 
case. 


—50— 

CASE  6-c.  —  It  is  a  convenience  in  dealing  with 
ciphers  made  up  of  numbers  or  conventional  signs  to 
substitute  arbitrary  letters  for  the  numbers  and 
signs.  Suppose  we  have  the  message: 

"??2&        45x15         )"8&#        &&lx4         %&4&% 
6x?&"         8&*x4        6°*°&        %"4&" 

By  arbitrary  substitution  of  letters  this  is 
made 

ABBCD      EFGHF      IJKDL     DDHGE      MDEDM      NGBDA 
KDOGE        NPOPD      MAEDA 

This  message  is  now  in  convenient  shape  to 
handle  as  Case  6-a  and  on  solution  is  found  to  read: 

ALL  PERSONS  HAVE  BEEN  ORDERED  TO  LEAVE  FOR- 
TIFIED AREA. 

In  the  same  way  the  message 

1723  3223  2825  1828  3630  2336  1423  2827  2324  3120  2317  3123 
3036  2120  2415  3029  1512  2831  1721  2715  2811  2715  1923  3030 
1215  1130  2128  3623 

is  found  to  be  made  up  entirely  of  numbers  between 
11  and  36  with  the  numbers  23,  28  and  30  occurring 
most  frequently.  This  immediately  suggests  an 
alphabet  made  up  of  the  numbers  from  11  to  36  in- 
clusive and  each  cipher  group  of  figures  represents 
two  letters.  By  arbitrary  substitution  of  letters  for 
groups  of  two  numbers  we  obtain: 

AB  CB  DE  FD  GH  BG  IB  DJ  BK  LM  BA  LB 
HG  NM  OP  HQ  PR  DL  AN  JP  DS  JP  TB  HH 
RP  SH  ND  GB 

and  this  message  is  also  in  shape  to  handle  as  Case 
6-a.  It  reads,  on  solution, 

SEVEN    HUNDRED    MEN    LEFT    YESTERDAY    FOR 
POINTS  ON  LOWER  RIO  GRANDE. 


Chapter  VII 


WILL  now  consider  the  class  of  substitution 
ciphers  where  a  number  of  alphabets  are 
used,  the  number  and  choice  of  alphabets  depending 
on  a  key  word  or  equivalent  and  being  used  periodi- 
cally throughout  the  message. 

In  this  class  belong  the  methods  of  Vigenere, 
Porta,  Beaufort,  St.  Cyr,  and  many  others.  These 
methods  date  back  several  hundred  years,  but  varia- 
tions of  them  are  constantly  appearing  as  new 
ciphers.  The  Larrabee  cipher,  used  for  communica- 
tion between  government  departments,  is  the  Vige- 
nere cipher  of  the  17th  Century.  The  cipher  disk 
method  is  practically  the  Vigenere  cipher  with 
reversed  alphabets. 

In  using  these  ciphers,  there  is  provided  a  num- 
ber of  different  cipher  alphabets,  usually  twenty-six, 
and  each  cipher  alphabet  is  identified  by  a  different 
letter  or  number.  A  key  word  or  phrase  (or  key 
number)  is  agreed  upon  by  the  correspondents.  The 
message  to  be  enciphered  is  written  in  lines  contain- 
ing a  number  of  letters  which  is  a  multiple  of  the 
number  of  letters  of  the  key.  The  key  is  written  as 
the  first  line.  Then  each  column  under  a  letter  of 
the  key  is  enciphered  by  the  cipher  alphabet  pertain- 
ing to  that  letter  of  the  key.  For  example,  let  us 
take  the  message,  "All  radio  messages  must  here- 
after be  put  in  cipher/'  with  the  key  GRANT,  using 
the  Vigenere  cipher  alphabets  given  below.  Each  of 
these  alphabets  is  identfied  by  the  first  or  left  hand 
letter  which  represents  A  of  the  text.  We  thus  will 

51 


—52— 

use  in  turn  the  alphabets  beginning  with  G,  with  R, 
with  A,  with  N,  and  with  T. 

GR ANTGRANT 

ALL  R ADI  OME 
S  S A  GE  SMUS  T 
HER  E AFT  ER  B 
EPUTINCIPH 
ER 

Using  the  alphabet  indicated  by  G,  we  get 

G  J 

Y  Y 

N  L 

K  T 

K 

Continuing  for  the  other  alphabets,  we  get 

GCLETJZOZX 
Y  J  AT  X YDUFM 
N VRRT  LKEE  U 
KGUGBTTICA 
KI 

This  method  of  arranging  the  message  into  lines 
and  columns  and  then  enciphering  whole  columns 
with  each  cipher  alphabet  is  much  shorter  than  the 
method  of  handling  each  letter  of  the  message  sep- 
arately. The  chance  of  error  is  also  greatly  reduced. 

All  these  cipher  methods  can  be  operated  by 
means  of  squares  containing  the  various  alphabets, 
cipher  disks  or  arrangements  of  fixed  and  sliding 
alphabets.  For  example,  this  was  the  original  cipher 
of  Vigenere: 


(See  next  page.) 


—53— 


ABODEFGHIJKLiMNOPQRSTUVWXYZ 
BCDEFGH  IJKLMNO  PQRSTUVWXYZA 
CDEFGHI  JKLMNOPQKSTUVWXYZAB 
DEFGHI  JKLMNOPQR  STUVWXYZABC 
EFGHIJKLMNOPQRSTUVWX  Y  ZABCD 
FGHI  JKLMNOPQRSTUVWXYZ  ABODE 
GHIJKLMNOPQRSTUVWXYZA  B  CDEF 
HIJKLMNOPQRSTUVWXYZA  B  CDEFG 
I  JKLMNOPQRSTUVWXYZABCDEFGH 
JKLMNOPQRSTUVWXYZABCDE  F  GH  I 
KLMNOPQRSTUVWXYZAB CDEFGHI J 
LMNOP  QRSTUVWXYZABCDEFGHI  JK 
M  N  O  PQRSTUVWXYZA  BODE  F  GH  I  JKL 
NOPQRS  TUVWXYZABCDEFGH  I  JKLM 
OPQRSTUVWXYZABODEFGH I JKLMN 
PQRSTUVWXYZABO  DEFGHI  JKLMNO 
QRSTUVWXYZABCDEFGH  I  JKLMNO  P 
RSTUVWXYZABCDEFGHI  JKLMNO  PQ 
STUVWXYZ  ABODE  FGHI  JKLMNO  P  QR 
TUVWXYZABODEFGH1JKLMNOP  QR  S 
UVWXYZABODEFGH IJKLMNO PQRST 
VWXYZABCDEFGHI  JKLMN  O  P  QRSTU 
WXYZABODEFGHI  JKLMNOP  QRSTUV 
XYZABCDEFGHIJKLMNOPQRSTU  V  W 
YZABCDEFGHIJKLMNOPQ  RSTUVWX 
ZABCDEFGHIJKLMNOPQRSTUVWXY 

The  first  horizontal  alphabet  is  the  alphabet  of 
the  plain  text.  Each  substitution  alphabet  is  desig- 
nated by  the  letter  at  the  left  of  a  horizontal  line. 
For  example,  if  the  [key  word  is  BAD,  the  second, 
first  and  fourth  alphabets  are  used  in  turn  and  the 
word  WILL  is  enciphered  XIOM. 

The  Larrabee  cipher  is  merely  a  slightly  different 
arrangement  of  the  Vigenere  cipher  and  is  printed 
on  a  card  in  this  form: 


(See  next  page.) 


—54— 

CLMN 
abed  efghij   klmnopqrs  tuv  wxy  z 


\     AB  C  DE  FG  HI  JKLMNO  P  Q  RSTU  V  WX  YZ 


BABCDEFGHIJKLMNOPQRSTUVWXYZ 
bcdefghijklmnopqrstuvwxy    z    a 


CABCDEFGHIJKLMNOPQRSTUVWXYZ 
c    defgh   i    jklmnopqr   s   t   uvwxyz   ab 

etc. 

YABCDEFGHIJKLMNOPQRSTUVWXYZ 
yzabcd  e    fghi   j  klmnopqrs   t   u   vwx 

ZABCDEFGHIJKLMNOPQRSTUVWXYZ 
zabcd  efghij    klmnopqrstuvwxy 

The  large  letters  at  the  left  are  the  letters  of 
the  key  word.  It  will  be  noted  that  these  letters 
correspond  to  the  first  letters  of  the  cipher  alphabets 
( in  small  letters)  as  in  the  Vigenere  cipher. 

A  much  simpler  arrangement  of  the  Vigenere 
cipher  is  the  use  of  a  fixed  and  sliding  alphabet. 
Either  the  fixed  or  sliding  alphabet  must  be  double 
in  order  to  get  coincidence  for  every  letter  when  A  is 
set  to  the  letter  of  the  key  word. 

Fixed  Alphabet  of  Text 

ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNO  PQRSTUV  WXYZ   ! 


ABCDEFGHIJKLMNOPQRSTUVWXYZ 

Movable  Alphabet  of  Cipher 


As  shown  here,  A  of  the  fixed  or  text  alphabet 
coincides  with  T  of  the  movable  cipher  alphabet. 
This  is  the  setting  where  T  is  the  letter  of  the  key 
word  in  use.  The  lower  movable  alphabet  is  moved 
for  each  letter  of  the  message  and  the  A  of  the  fixed 
alphabet  is  made  to  coincide  in  turn  with  each  letter 
of  the  key  before  the  corresponding  letter  of  the 
text  is  enciphered.  It  is  obviously  only  a  step  from 
this  arrangement  to  that  of  a  cipher  disk,  where  the 


—55— 

fixed  alphabet,  (a  single  one  will  now  serve)  is  printed 
in  a  circle  and  the  movable  alphabet,  also  in  a  circle, 
is  on  a  separate  rotatable  disk.  Coincidence  of  any 
letter  on  the  disk  with  A  of  the  fixed  alphabet  is  ob- 
tained by  rotating  the  disk. 

The  well  known  U.  S.  Army  Cipher  Disk  has  just 
such  an  arrangement  of  the  fixed  alphabet  but  the 
alphabet  of  the  disk  is  reversed.  This  has  several 
advantages  in  simplicity  of  operation  but  none  in  in- 
creasing the  indecipherability  of  the  cipher  prepared 
with  it.  The  arrangement  of  fixed  and  sliding  alpha- 
bets which  is  equivalent  to  the  U.  S.  Army  cipher 
disk  is  this: 

Fixed  Alphabet 

ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ 


ZYXWVUTSRQPONMLKJIHGFEDCBA 

Movable  Alphabet 


It  will  be  noticed  that  with  this  arrangement  of 
running  the  alphabets  in  opposite  directions,  it  be- 
comes immaterial  which  alphabet  is  used  for  the 
text  and  which  for  the  cipher  for  if  A— G  then  G= A. 
This  is  not  true  of  the  Vigenere  cipher. 

It  is  perfectly  feasible  to  substitute  a  card  for 
the  U.  S.  Army  cipher  disk.  It  would  have  this 
form: 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 

1  AZYXWVUTSRQPONMLKJIHGFEDCB 

2  BAZYXWVUTSRQPONMLKJIHGFEDC 

3  CBAZYXWVUTSRQPONMLKJIHGFED 

etc. 

25  YXWVUTSRQPONMLKJIHGFEDCBAZ 

26  ZYXWVUTSRQPONMLKJIHGFEDCBA 

The  first  horizontal  line  is  the  alphabet  of  the 
text.  The  other  twenty-six  lines  are  the  cipher  al- 
phabets each  corresponding  to  the  letter  of  the  key 
word  which  is  at  the  left  of  the  line. 


—56— 

One  of  the  ciphers  of  Porta  was  prepared  with  a 
card  of  this  kind: 


\  O 
-f*  t> 


ABCDEFGHIJKLM 
NOPQRSTUVWXYZ 


ABCDEFGHIJK  LM 
ZNOPQRSTUVWXY 

ABCDEFGHIJKLM 
YZ ABCDEFGHIJK 


EF 


etc. 


Y 
-A. 


ABCDEFGHIJKLM 
PQRSTUVWXYZNO 

ABCDEFGHIJKLM 
O  PQRS  TU  VWXYZN 

In  this  cipher  the  large  letters  at  the  left  cor- 
respond to  the  letters  of  the  key  and,  in  each  alpha- 
bet, the  lower  letter  is  substituted  for  the  upper  and 
vice  versa.  For  example,  with  key  BAD  to  encipher 
WILL  we  would  get  JVXY.  Note  that  with  either  B 
or  A  as  the  key  letter,  the  first  alphabet  would  be 
used. 

A  combination  of  the  Vigenere  and  Porta  ciphers 
is  this: 

AABODEFGHIJKLMNOPQRSTUVWXYZ 
ABCDEFGHIJKLMNOPQRSTUVWXYZ 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 
BCDEFGHIJKLMNOPQRSTUVWXYZA 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 
CDEFGHIJKLMNOPQRSTUVWXYZAB 

etc. 

T  TTT  r    ABCDEFGHIJKLMNOPQRSTUVWXYZ 
V    VV     LMNOPQRSTUVWXYZABCDEFGHIJK 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 
MNOPQRSTUVWXYZABCDEFGHIJKL 

ABCDEFGHIJKLMNOPQRSTUVWXYZ 
NOPQRSTUVWXYZABCDEFGHIJKLM 


—57— 

Here  again  the  large  letters  at  the  left  corres- 
pond to  the  letters  of  the  key  and,  in  each  pair  of 
alphabets,  the  upper  one  is  that  of  the  plain  text  and 
the  lower  is  that  of  the  cipher, 

This  cipher  can  also  be  operated  by  a  fixed  and 
sliding  alphabet. 

Fixed  Alphabet  of  Text: 

ABCDEPGHIJKLMNOPQRSTUVWXYZABCDEPGHIJKLMNOPQRSTUVWXYZ 


ABCDEFGHIJKLMNOPQRSTUVWXYZ 

Sliding  Alphabet  of  Cipher 
Index 


BDFHJLNPRTVX 

A  Z  Letters  of  Key. 

CEGIKMOQSUWY 

The  other  ciphers  mentioned  are  merely  varia- 
tions of  these  that  have  been  discussed.  It  is  im- 
material, in  the  following  analysis,  which  variety  has 
been  used.  The  analysis  is  really  based  on  what  can 
be  done  with  a  cipher  made  up  with  a  mixed  cipher 
alphabet  which  may  be  moved  with  reference  to  the 
fixed  alphabet  of  the  text,  (See  Case  7-b).  Clearly 
this  is  a  much  more  difficult  proposition  than  dealing 
with  a  cipher  in  which  the  cipher  alphabets  run  in 
their  regular  sequence,  either  backward  or  forward. 
In  fact,  in  the  analysis  of  Case  7,  we  may  consider 
any  cipher  prepared  by  the  method  of  Vigenere  or 
any  of  its  variations  as  a  special  and  simple  case. 

It  was  long  ago  discovered  that,  in  any  cipher  of 
this  class,  (1)  two  like  groups  of  letters  in  the  cipher 
are  most  probably  the  result  of  two  like  groups  of 
letters  of  the  text  enciphered  by  the  same  alphabets 
and  (2)  the  number  of  letters  in  one  group  plus  the 
number  of  letters  to  the  beginning  of  the  second 
group  is  a  multiple  of  the  number  of  alphabets  used. 
It  is  evident,  of  course,  that  we  may  have  similar 
groups  in  the  cipher  which  are  not  the  result  of  en- 


—58— 

ciphering  similar  groups  of  the  text  by  the  same 
alphabets  but  if  we  take  all  recurring  groups  in  a 
message  and  investigate  the  number  of  intervening 
letters,  we  will  find  that  the  majority  of  such  cases 
will  conform  to  these  two  principles. 

Changing  the  key  word  and  message  to  illustrate 
more  clearly  the  above  points,  the  following  is  quoted 
from  the  Signal  Book,  1914,  with  reference  to  the 
use  of  the  cipher  disk  in  preparing  a  message  with  a 
key  word.* 

-This  simple  disk  can  be  used  with  a  cipher 
word  or,  preferably,  cipher  words,  known  only  to  the 
correspondents Using  the  key  word  'disk'  to  en- 
cipher the  message  'Artillery  commander  will  order 
all  guns  withdrawn,'  we  will  proceed  as  follows: 
Write  out  the  message  to  be  enciphered  and  above  it 
write  the  key  word....  letter  over  letter,  thus: 


DISK 
ARTI 


DISK     DISK]    DISK     DISK  j    DISK!    DISK     DISK     DISK 


LLEB   YCOM' MANDJ  ERWI     LLOR   DERA     LLGU 


SXOT 


NSWI 


FGEYj   RIFHiZRWCJ    SXET,   AEBK   SXMQl  QQW 


DIS 
AWN 


Cj 


"Now  bring  the  V  of  the  upper  disk  under  the 
first  letter  of  the  key  word  on  the  lower  disk,  in  this 
case  'D'.  The  first  letter  of  the  message  to  be  en- 
ciphered is  'A':  'd'  is  found  to  be  the  letter  con- 
nected with  'A',  and  it  is  put  down  as  the  first  cipher 
letter.  The  letter  'a'  is  then  brought  under  T  which 
is  the  second  letter  of  the  key  word.  *R'  is  to  be 
enciphered  and  V  is  found  to  be  the  second  cipher 

letter Proceed  in  this  manner  until  the  last 

letter  of  the  key  word  is  used  and  beginning  again 
with  the  letter  T)',  so  continue  until  all   letters  of 

*The  method  used  is  nob  the  most  satisfactory  one  for 
several  reasons  and  a  better  method  is  that  of  writing  the 
message  in  multiples  of  the  key  and  enciphering  the  columns 
as  already  described. 


—59— 

the   message   have  been   enciphered.     Divided  into 
groups  of  five  letters,  it  will  be  as  follows: 

"DRZCS    XOTFG    EYRIF    HZRWC     SXETA    EBKSX 
MQQQW  CKBPT  DMF." 

So  much  for  the  Signal  Book;  now  let  us  ex- 
amine the  above  message  for  pairs  or  similar  groups 
and  count  the  intervening  letters  to  demonstrate 
principles  (1)  and  (2); 

CSX^CSX  16=4x4 

SX—    SX  16=4x4 

SX—    SX  8=2x4 

WC— WC  16=4x4 

The  key  word  might  contain  2,  4  or  8  letters 
from  the  evidence  but  we  may  eliminate  2  as  un- 
likely and  preparation  of  frequency  tables  of  each  of 
the  four  alphabets  would  soon  show  that  4  is  the 
correct  number. 

A  later  and  more  extensive  example  (Case  7-a) 
will  show  pairs  not  separated  by  multiples  of  the 
number  of  alphabets  used,  but  the  evidence  in  nearly 
every  case  will  be  practically  conclusive.  Especially 
is  this  so  if  chance  assists  us  by  giving  groups  of 
three  or  more  letters  like  the  group  CSX  in  the 
above  example.  The  number  of  alphabets  having 
been  determined  each  alphabet  is  handled  by  the 
methods  of  Case  6  already  discussed. 

CASE  7-a.— The  following  message  appeared  in 
the  "personal"  column  of  a  London  paper: 

"M.  B.  Will  deposit  £27  14s  5d  tomorrow," 
and  the  next  day  we  find  this  one: 


(Cipher  on   next  page.) 


—60— 

M.B.  CT  OSB  UHGI  TP  IPEWF  H 
CEWIL  NSTTLE  FJNVX  XTYLS  FWKKHI 
BJLSI  SQ  VOI  BKSM  XMKUL  SK  NVP- 
ONPN  GSW  OL.  IEAG  NPSI  HYJISFZ 
CYY  NPUXQG  TPRJA  VXMXI  AP  EHV- 
PPR  TH  WPPNEL.  UVZUA  MMYVSF 
KNTS  ZSZ  UAJPQ  DLMMJXL  JR  RA 
PORTELOGJ  CSULTWNI  XMKUHW 

XGLN  ELCPOWY  OL.  ULJTL  BVJ 
TLBWTPZ  XLD  K  ZISZNK  OSY  DL 
RYJUAJSSGK.  TLFNS  UV  D  VV  FQGCYL 
FJHVSI  YJL  NEXV  PO  WTOL  PYYYHSH 
GQBOH  AGZTIQ  EYFAX  YPMP  SQA 
CI  XEYVXNPPAII  UV  TLFTWMC  FU 
WBWXGUHIWU.  AIIWG  HSI  YJVTI 
BJV  XMQN  SFX  DQB  LRTY  TZ 

QTXLNISVZ.  GIFT  All  UQSJGJ  OHZ 
XFOWFV  BKAI  CTWY  DSWTLTTT- 
PKFRHG  IVX  QCAFV  TP  DIIS  JBF 
ESF  JSC  MCCF  HNGK  ESBP  DJPQ 
NLU  CTW  ROSE  OSM. 

The  messages  in  question  appeared  in  an  Eng- 
lish newspaper.  It  is  fair  to  presume  then  that  the 
cipher  is  in  English.  This  is  checked  negatively  by 
the  fact  that  it  contains  the  letter  W  which  is  not 
used  in  any  of  the  Latin  languages  and  that  the  last 
fifteen  words  of  the  message  consist  of  from  two  to 
four  letters  each,  an  impossible  thing  in  German. 
It  contains  108  groups  which  are  probably  words,  as 
there  are  473  letters  or  an  average  of  4.4  letters  per 
group,  while  we  normally  expect  an  average  of 
about  5  letters  per  group.  The  vowels  AEIOU  num- 
ber 90  and  the  letters  JKQXZ  number  78.  It  is  thus 
a  substitution  cipher  (20%  of  473=94.6). 

Recurring  words  and  similar  groups  are  AIIWG, 
All;  BKSM,  BKAI;  CT,  CTWY,  CTW;  DLMMJXL, 
DL;  ESF,  ESBP;  FJNVX,  FJHVSI;  NPSI,  NPUXQG; 
OSB,  OSY,  ROSE;  OL,  OL;  PORTELOGJ,  PO;  SQ, 
SQA;  TP,  TP;  TLBWTPZ,  TLFNS,  TLFTWMC; 
UVZUA,  UVD,  UV;  XMKUL,  XMKUHW;  YJL, 
YJVTI. 


-  Gl    - 
Frequency  Table  for  the  Message 


ABCDEFGHIJKLMNOPQR 

15  13  15   8  13  20  16  16  30  21  13  27  14  19  15  26  13    9  ; 


STUVWXYZ 

!3  30  17  12   19    20    19  11 


This  clearly  eliminates  Cases  4,  5  and  6. 

Referring  to  the  recurring  words  and  groups 
above  noted,  we  figure  the  number  of  letters  be- 
tween each. 


All...  All 

45=3  x  3  x  5 

OSB. 

..OSB 

465=31  x  3  x  5 

BK...BK 

345=23x3x5 

PO 

...PO 

105=7  x  3  x  5 

CT  .  .  .  C  T 

403    No  factors 

SQ 

..SQ  . 

250=2  x  5  x  5  x  5 

CTW...CTW 

60=2  x  2  x  3  x  5 

TLF 

...TLF 

80=2  X2'x2x2x5 

DL...DL 

75=3  x  5  x  5 

TP. 

..TP 

405=3  x3x3x3x5 

ES...ES 

14=-2  x  7 

UV. 

..UV 

115=23  x  5 

FJ...FJ 

187    No  factors 

XMKU. 

..XMKU 

120=2  X2x2x3x5 

NP...NP 

14=2  x  7 

UV. 

.UV, 

73    No  factors 

OL...OL 

120=2  X2x2x3x5 

YJ. 

..YJ 

85=17  x  5 

OS.  ..OS 

220=11  x  2x2x5 

The  dominant  factor  is  clearly  5,  so  we  may  con- 
sider that  five  alphabets  were  used,  indicating  a  key- 
word of  five  letters.  Writing  the  message  in  lines 
of  five  letters  each  and  making  a  frequency  table  for 
each  of  the  five  columns  so  formed,  we  find  the  fol- 
lowing: 

Frequency    Tables 


Colum 

Column  2 

Column  3 

Column  U 

Column  5 

A  11 

A  111111111 

A  1 

A  1 

A  11 

B 

B  111 

B  111 

B 

B  1111111 

C  1111111 

C  1 

C  111 

C  1111 

C 

D  11 

D  11 

D  1 

D 

D  111 

E  1111 

E 

E  11 

E  1111111 

E 

F  111 

F 

F  11111111] 

F  III 

F  11111 

G  111111111-G 

G  111 

G  II 

G  11 

H  111 

H  11111 

H  111 

H  111 

H  11 

I  11 

I  11 

I  1111111 

I  11111111111111111 

I  11 

J  11111 

J  1 

J  111111 

J 

J  111111111 

K  mm 

K  11111 

K 

K  1 

K  1 

L 

L  1111111111111111 

L11L  11 

L  urn 

L  1 

M 

M 

M  1111111 

MIIII 

Mill 

N  1111111 

N  111 

N  1111 

N 

N  urn 

O  11111 

0 

O  111111111 

0  1 

0 

P  1111111 

P  1111111 

P  11111111 

P  1111 

P 

§11111 

Q 

Q 

Q  11 

gllllll 

R  1 

R  1 

R  Him 

1 

S 

S  11111111 

s  Him 

S  111111111111 

S  1111111 

T  1111111 

T  111 

T  inn 

T  1 

T  11111111111111 

U  1111111 

U  111 

u  mm 

u 

U  1 

V  11111 

V 

V  II 

v  mil 

V 

Will 

Wllll 

w 

w  urn 

W  1111111 

X  11 

x 

X  1111 

X  11111111 

x  iiim 

Y  1111 

Y  11111 

Y 

Y  111 

Y  1111111 

Z 

Z  11111 

Z  111 

Z 

Z  111 

In  the  table  for  Column  1,  the  letter  G  occurs   9 


—62— 

times.  Let  us  consider  it  tentatively  as  E.  Then  if 
the  cipher  alphabet  runs  regularly  and  in  the  direc- 
tion of  the  regular  alphabet,  C  (7  times) = A  and  the 
cipher  alphabet  bears  a  close  resemblance  to  the 
regular  frequency  table.  Note  TUV  (=RST)  occur- 
ring respectively  7,  7,  and  5  times  and  the  non-occur- 
rence of  B,  L,  M,  R,  S,  Z,  (=Z,  J,  K,  P,  Q,  and  X 
respectively. ) 

In  the  next  table,  L  occurs  19  times  and  taking 
it  for  E  with  the  alphabet  running  in  the  same  way, 
A=H.  The  first  word  of  our  message,  CT,  thus  be- 
comes AM  when  deciphered  with  these  two  alphabets 
and  the  first  two  letters  of  the  key  are  C  H. 

Similarly  in  the  third  table  we  may  take  either 
F  or  0  for  E,  but  a  casual  examination  shows  that  the 
former  is  correct  and  A=B  (even  if  we  were  looking 
for  a  vowel  for  the  next  letter  of  the  keyword). 

In  the  fourth  table,  I  is  clearly  E  and  A=E.  The 
fifth  table  shows  T=14  and  J=9.  If  we  take  T=E 
we  find  that  we  would  have  many  letters  which 
should  not  occur.  On  the  other  hand,  if  we  take 
J=E  then  T=0  and  in  view  of  the  many  E's  already 
accounted  for  in  the  other  columns,  this  may  be  all 
right.  It  checks  as  correct  if  we  apply  the  last  three 
alphabets  to  the  second  word  of  our  message,  OSB, 
which  deciphers  NOW.  Using  these  alphabets  to 
decipher  the  whole  message,  we  find  it  to  read: 

'  'M.  B.  Am  now  safe  on  board  a  barge  moored 
below  Tower  Bridge  where  no  one  will  think  of  look- 
ing for  me.  Have  good  friends  but  little  money 
owing  to  action  of  police.  Trust,  little  girl,  you  still 
believe  in  my  innocence  although  things  seem  against 
me.  There  are  reasons  why  I  should  not  be  ques- 
tioned. Shall  try  to  embark  before  the  mast  in  some 
outward  bound  vessel.  Crews  will  not  be  scrutinized 
so  sharply  as  passengers.  There  are  those  who  will 
let  you  know  my  movements.  Fear  the  police  may 


—63— 

tamper  with  your  correspondence  but  later  on  when 
hue  and  cry  have  died  down  will  let  you  know  all." 

The  key  to  this  message  is  CHBEF  which  is  not 
intelligible  as  a  word  but  if  put  into  figures  indicating 
that  the  2d,  7th,  1st,  4th,  and  5th  letter  beyond  the 
corresponding  letter  of  the  message  has  been  used 
the  key  becomes  27145  and  we  may  connect  it  with 
the  "personal"  which  appeared  in  the  same  paper 
the  day  before  reading: 

"M.  B.     Will  deposit  £27  14s  5d  tomorrow." 

CASE  7-b 

Message 

DDLRM  ERGLM  UJTLL  CHERS  LSOEE  SMEJU 
Z  JIMU  DAEES  DUTDB  GUGPN  RCHOB  EQEIE 
OOACD  EIOOG  COLJL  PDUVM  IGIYX  QQTOT 
DJCPJ  OISLY  DUASI  UPFNE  AECOB  OESHO 
BETND  QXUCY  LUQOY  EHYDU  LXPEQ  FIXZE 
PDCNZ  ENELQ  MJTSQ  ECFIE  ARNDN  ETSCF 
IFQSE  TDDNP  UUZHQ  CDTXQ  IRMER  GLXBE 
IQRXJ  FBSQD  LDSVI  XUMTB  AEQEB  YLECO 
I YCUD  QTPYS  VOQBL  ULYRO  YHEFM  OYMUY 
ROYMU  EQBLV  UBREY  GHYTQ  CMUBR  EQTOF 
VSDDU  DAFFS  CEBSV  TIOYE  TCLQX  DVNLQ 
XYTSI  MZULX  BAXQR  ECVTD  ETGOB  CCUYF 
TTNXL  UNEFS  IVIJR  ZHSBY  LLTSI 

On  the  preliminary  determination,  we  have  the 
following  count  of  letters  out  of  a  total  of  385: 

A 
I 


Total 


Every  letter  except  K  and  W  occurs  at  least  six 
times.  We  may  say  then  that  it  is  a  substitution 
cipher,  Spanish  text,  and  certainly  not  Case  4,  5  or  6. 
We  will  now  analyze  it  for  recurring  pairs  or  groups 


L    8 

L  23 

J  9 

!  38 

N  11 

Q  22 

19 

R  14 

V  9 

'  21 

S  20 

X  13 

r  24 

T  21 

Z  6 

110   Total 

89 

Total    59 

28% 

23% 

15% 

to  determine,  if  it  be  Case  7,  how  many  alphabets 
were  used.  The  following  is  a  complete  list  of  such 
recurring  groups  and  pairs  with  the  number  of  letters 
intervening  and  the  factors  thereof.  In  work  of  this 
kind,  the  groups  of  three  or  more  letters  are  always 
much  more  valuable  than  single  pairs.  For  example, 
the  groups,  HOBE,  OYMU,  RMERGL  and  UBRE 
show,  without  question,  that  six  alphabets  were  used. 
It  is  not  necessary,  as  a  rule,  to  make  a  complete  list 
like  the  following: 


AE     74=2x37 
AE  120=2x2x2x3x5 
BE     88=2x2x2x11 
CD  132=2x2x3x11 
CFI     12=2x2x3 
CH     36=2x2x3x3 
CO     42=2x3x7 
CO  126=2x3x3x7 
CU  114=2x3x19 
DD  186=2x3x31 
DD  116=2x2x29 
DE  285=5x57 
DL  218=2x109 
DN     14=2x7 
DQ  120=2x2x2x3x5 
DU     36=2x2x3x3 
DU     24=2x2x2x3 
DU    38=2x19 
DU  165=3x5x11 
EA    30=2x3x5 
EB     78=2x3x13 
EC  180=2x2x3x3x5 


IE  110=2x5x11  RE     50=2x5x5 

IM  302=2x151  RMERGL  198=2x3x3x11 


IO  250=2x5x5x5 
IX    78=2x3x13 
LY  158=2x79 
JT  150=2x3x5x5 
LL  367  No  factors 
LQ  164=2x2x41 
LQX       6=2x3 
LU  124=2x2x31 
LU  110=2x5x11 
LU  234=2x3x3x13 
LX     66=2x3x11 
LXB  132=2x2x3x11 
LY  158=2x79  TD  165=3x5x11 

ME     22=2x11         TD     96=2x2x2x2x2x3 
MU    24=2x2x2x3        TN  239  No  factors 
MU  240=2x2x2x2x3x5  TS     14=2x7 
MU     18=2x3x3  TS  156=2x2x3x13 

ND    47  No  factors     TSI    50=2x5x5 
NE     48=2x2x2x2x3  UBRE     12=2x2x3 
NE     18=2x3x3  UD     60=2x2x3x5 


SC  132=2x2x3x11 
SD  262=2x131 
SI  230=2x5x23 
SI     34=2x17 
SI  264=2x2x2x3x11 
SI     12=2x2x3 
78=2x3x  13 
54=2x3x3x3 
27=3x3x3 
63=3x3x7 
90=2x3x3x5 
47  No  factors 


SL 
SQ 

SV 

sv 

SV 
TD 


ECO  126=2x3x3x7  NE  192-2x2x2x2x2x2x3  UDA  270-2x3x3x3x5 


EES    14=2x7 
EF  105=3x5x7 
El       8=2x2x2 
El  152=2x2x2x19 
EQ    88=2x2x2x11 


OB      6=2x3  UL  114=2x3x19 

OB  234=2x3x3x13  ULX  198=2x3x3x11 
OE     93=3x31  UY     89  No  factors 

UZ  162=2x3x3x3x3 
VI  148=2x2x37 


OI  144=2x2x2x2x3x3 
OO      7  No  factors 


EQ  264=2x2x2x3x11    OY       6=2x3 
EQ    44=2x2x11  OY     46=2x23 

EQE  176=2x2x2x2x11  OYMU  6=2x3 


VT     33=3x11 
XQ  114=2x3x19 
XQ  144=2x2x2x2x3x3 


—65— 

ER    12=2x2x3  PD    75=3x5x5           XU    99=3x3x11 

ES     78=2x3x13  QBL     24=2x2x2x3        YE  184=2x2x2x23 

ET  135=3x3x5  QC     95=5x19                YL  106=2x53 
ET       9=3x3           QE  108=2x2x3x3x3     YL  144=2x2x2x2x3x3 

ET    54=2x3x3x3  QE     68=2x2x17          YM      6=2x3 

ET    31  No  factors  QR  132=2x2x3x11  YRO     12=2x2x3 

HE  245=5x7x7  QTO  210=2x3x5x7         ZE       6=2x3 

KOBE  66=2x3x11  QX  198=2x3x3x11      ZH  183=3x61 

Out  of  one  hundred  and  one  recurring  pairs  we 
have  fifty  with  the  factors  2x3=6;  out  of  twelve  re- 
curring triplets,  nine  have  these  factors;  and  the 
four  recurring  groups  of  four  or  more  letters  all  have 
these  factors.  The  percentages  are  respectively 
49.5%,  75%  and  100%  and  we  may  be  certain  from 
this  that  six  alphabets  were  used.  But,  before  the 
six  frequency  tables  are  made  up,  there  is  one  more 
point  to  be  considered;  why  are  there  so  many  re- 
curring groups  which  do  not  have  six  as  a  factor? 
The  answer  is  that  one  or  more  of  the  alphabets  is 
repeated  in  each  cycle;  that  is,  a  key  word  of  the 
form  HAVANA  has  been  used.  If  this  were  the  key 
word,  the  second,  fourth  and  sixth  alphabets  would 
be  the  same.  We  will  see  later  that  in  this  example 
the  second  and  sixth  alphabets  are  the  same  and  this 
introduces  the  great  number  of  recurring  groups 
without  the  factor  6. 

We  will  now  proceed  to  make  a  frequency  table 
for  each  alphabet.  As  the  message  is  written  in 
thirty  columns,  we  take  the  first,  seventh,  thirteenth, 
etc.,  as  constituting  the  first  alphabet;  the  second, 
eighth,  fourteenth,  etc.,  as  constituting  the  second 
alphabet  and  so  on.  The  prefix  and  suffix  letter  is 
noted  for  each  occurrence  of  each  letter.  The  im- 
portance of  this  will  be  appreciated  when  the  form 
of  the  frequency  tables  is  examined.  None  bears 
any  resemblance  to  the  normal  frequency  table  ex- 
cept that  each  is  evidently  a  mixed  up  alphabet.  The 


—66— 

numbers  after  "Prefix"  and  "Suffix"  refer  to  the 
alphabet  to  which  these  belong,  for  convenience  in 
future  reference. 

Frequency  Tables 

FIRST  ALPHABET  SECOND  ALPHABET 


Letter 

Prefix  (6) 

Suffix  (^ 

Letter 

Prefix  (1) 

Suffix  (3) 

A  111 

3  DUD 

ESF 

A 

0 

B  11111111 

8000FEEOS 

EOESYSCY 

B  111 

3  TQQ 

ALL 

C 

0 

C  1 

1   B 

C 

D  1111 

4TYT 

DJUD 

D  111111 

6   DTPDXT 

LBCNVE 

E  1 

IE 

S                            E  11111111111  11   ABNBNINRRYN  EOATLATYQTF 

F 

0 

F  111 

3  QIA 

IQF 

G 

0 

G  11 

2  RR 

LL 

H 

0 

H  1 

1  Z 

0 

I    11111111 

SEOFFEOVS 

OSEFQYJ 

I 

0 

J 

0 

J    1111 

4  ZLDI 

ILCR 

L  1 

lo 

J 

L  1 

IT 

L 

Ml 

1  F 

o 

Ml 

1  V 

I 

N  1111 

4FEDU 

EEEE 

Nl 

IP 

R 

O  1 

IE 

o 

O  1111111 

7   OIBQRMR 

AOEYYYY 

P  11 

2GE 

ND 

P  1 

IT 

Y 

Q  1111 

4UEOE 

OFBB 

Q  11111 

5  XXITX 

OIRCR 

R  1111111 

7  EEEYYBB 

GSGOOEE 

R 

0 

S  1 

ID 

V 

S  11111111 

8  REIATBVB 

LMLIQQDV 

T  11111111 

SJUJMQYVF  LDSBPQDT 

T  1 

IT 

N 

U 

0 

U  111 

3  XDZ 

CLL 

V  11 

2UF 

MS 

V  1 

1  s 

I 

X  111111 

6YQTQQA 

QUQDYQ 

X 

0 

Y  1 

lo 

E 

Y  1111 

4  BIXB 

LCTL 

Z  111 

3UUM 

JHU 

Z 

0 

THIRD  ALPHABET 


FOURTH  ALPHABET 


Letter 

Prefix  (2) 

Suffix  (4) 

Letter 

Prefix  (3 

Suffix  (;7) 

A 

1111 

4OEEB 

CERE 

A 

0 

B 

1 

ID 

G 

B 

0 

0 

imii 

6JUDYQC 

PYNUMU 

C 

11111 

5LRAQT 

HHDDL 

D 

1 

Is 

D 

D 

11 

2QD 

LU 

E 

111 

3EOD 

SST 

E 

11111111 

8  MQAYQALR 

JICHCQCC 

F 

11 

2FE 

SS 

F 

0 

G 

0 

G 

1111 

4BOIY 

UCIH 

H 

0 

H 

1 

lY 

E 

I 

111111 

6JMSFQV 

MGUXRX 

I 

0 

J 

0 

J 

0 

L 

11111111111111 

14  DGLSJSUEG 

RMCSPYXQ 

YBBUY 

XEUVXL 

L 

1 

1L 

T 

M 

1 

Is 

E 

M 

11111 

5LIYYC 

uuuuu 

N 

11 

2DT 

PX 

N 

111 

3TCV 

DZL 

0 

1 

lo 

G 

0 

0 

P 

0 

P 

111 

3LCN 

DJU 

Q 

1111111 

7EQSFHSE 

ETESCDT 

Q 

1 

1L 

M 

R 

1111 

4NQQJ 

CXEZ 

R 

111 

3  LAI 

MNM 

S 

0 

S 

111111111 

9LEETQYFTF 

ODHCEVCII 

T 

1111 

4EEEY 

NSCS 

T 

1111 

4QQVE 

OOIG 

U 

0 

U 

1111 

4ICLC 

PDLY 

V 

11 

2SD 

TN 

V 

1 

1L 

U 

X 

0 

X 

1111111 

7  LILRILN 

PZBUBL 

Y 

111111 

60POOOE 

ESHMMG 

Y 

11 

2  EC 

DLJ 

Z 

0 

Z 

1 

1R 

H 

—67— 


FIFTH  ALPHABET 


SIXTH  ALPHABET 


Letter 

Prefix  (4) 

Suffix  (6) 

Letter 

Prefix  (3) 

Suffix  (1) 

A 

0 

A  1 

IB 

X 

B  11 

2  xx 

EA 

B  11 

2uu 

RR 

C  1111111 

7GDDSDSD 

OOFPOEV 

C 

0 

D  111111 

6  SCPYNCU 

UEUUQTQ 

D  1111 

4UNLU 

ANSA 

E  11 

2SH 

TF 

E  1111111111111 

13MHOIDPZ 

RREOIQPN 

F 

0 

ZMBQUC 

RIBQB 

G  1 

lu 

T 

F  1111111 

7  PCCJEOC 

NIIBMVT 

H  111111 

6CCSDGZ 

EOOVYS 

G  1 

lu 

P 

I    11111 

5EGTSS 

EYOMV 

H 

0 

J  111 

3EPX 

UOF 

I 

0 

L  111111 

6YDUCNX 

UDYQQU 

J  11 

2UM 

TT 

Mill 

3RQR 

EJE 

L 

0 

N  1 

IB 

D 

M  11 

2ui 

TZ 

O  111 

3STT 

ETF 

N 

0 

P  11 

Oux 

FE 

O  111111111 

9HCJCHCVIG  BLIBBIQYB 

§1 

IE 

E 

P 

0 

0 

Q  1111 

4DDLL 

XTXX 

8 

0 

R 

0 

T  1 

IL 

S 

S  11 

2HT 

BI 

U  1111111111 

10MMGPXMM 

JDGUMYbB 

T  111 

30ED 

DDX 

VMD 

BD 

U  1111111 

7  JDDDLUL 

ZTVAQZN 

V  1 

Is 

O 

V  11 

2CI 

TI 

X 

0 

X 

Oi 

Y  1 

lu 

F 

Y  11111 

5  IHLUH 

XDRRT 

Z  11 

2XN 

EE 

Z 

0 

We  will  now  set  down  some  of  the  determina- 
tions which  can  be  made  at  once  from  these  fre- 
quency tables.  Clearly  several  mixed  alphabets 
have  been  used.  As  was  to  be  expected  from  the 
analysis  of  the  recurring  groups,  we  note  that  the 
frequency  tables  for  alphabets  2  and  6  are  of  so 
nearly  the  same  general  form  that  certainly  these 
two  alphabets  are  one  and  the  same.  If  a  Spanish 
word  has  been  used  as  a  key  word,  this  means  that 
A  is  probably  represented  by  a  vowel  in  these  two 
alphabets  and  probably  equals  A  or  0,  because  these 
two  letters  are  such  common  finals  in  Spanish. 

1st  Alphabet.  Probable  vowels  T,  X;  probable 
common  consonants,  B,  I,  N,  R.  We  conclude  this 
because  of  the  frequency  of  occurrence  of  T  and  X 
and  the  variety  of  their  prefixes  and  suffixes.  On 
the  other  hand,  B,  I,  N,  and  R  have  for  prefixes  and 
suffixes,  in  a  majority  of  cases,  E,  F,  0  and  S  which 
are  the  probable  vowels  in  the  2d  and  6th  alphabets. 

2d  and  6th  Alphabets.— Probable  vowels  E,  F,0, 
S;  probable  common  consonants,  D,  J,  Q,  U,  Y. 


—68— 

Sd^Alphabet.  —  Probable  vowels  C,  I,  L;  probable 
common  consonants  A,  Q,  T,  Y. 
:    :C4th  Alphabet.  -Probable   vowels,    E,    G,    S,  T; 
probable  common  consonants,  C,  M,  N,  P,  U,  X. 

5th  Alphabet.— Probable  vowels,  D,  L,  U;  prob- 
able common  consonants,  C,  H,  I. 

Now  this  cipher  may  have  been  made  up  from 
five  distinct  alphabets  with  letters  chosen  at  random 
but  it  is  much  more  likely  to  have  been  prepared 
with  a  cipher  disk  or  equivalent,  having  the  regular 
alphabet  on  the  fixed  disk  and  the  mixed  alphabet  on 
the  movable  disk.  An  equivalent  form  of  apparatus 
(not  using  the  mixed  alphabet  in  question)  is  one 
like  this: 

Fixed  Alphabet  of  Text 

ABCDEFGHTJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTTJVXYZ 


PCJVRQZBAODFSUTMXIYHLGEN 

Movable  Alphabet  of  Cipher 


Here  A  of  the  plain  text  is  enciphered  by  S  and  the 
other  letters  come  as  they  will.  If  we  move  the 
cipher  alphabet  one  space  to  the  left,  A  will  be  en- 
ciphered by  U  and  the  whole  sequence  of  the  alpha- 
bet will  be  changed. 

We  will  therefore  use  some  such  form  as  the 
above  and  see  if  we  can  insert  our  letters,  as  they 
are  determined,  in  such  a  way  as  to  have  each  of  the 
cipher  slips  identical.  We  may  start  thus: 

ABCDEFGHIJLMNOPQRSTUVXYZ AB  CD  EFGHIJLMNOPQRSTUVXYZ 

1st  Alphabet  t         x 

2d  ol     qei  ms       d  c  u 

3d  ol     qei    ms       d  c  u 

4th  ol    qei    ms       d  c  u 

5th  d   c    u  ol    qei    ms 

6th  o  1    qei  ms       d  c     u 

In  the  1st  alphabet,  T  and  X  are  placed  as  A  and 
E  respectively  on  the  basis  of  frequency.  In  the  2d 
and  6th  alphabets,  0  and  E  are  placed  as  A  and  E 
respectively  on  the  basis  of  frequency.  In  the  4th 


—69— 

alphabet,  E  and  S  are  placed  as  A  and  E,  and  in  the 
5th,  D,  U  and  L  are  placed  as  A,  E  and  0  for  the 
same  reason.  We  now  have  an  excess  of  E's  and  a 
deficiency  of  A's,  which  will  be  corrected  if,  in  the 
3d  alphabet,  we  place  L,  I  and  C  as  A,  E  and  0  re- 
spectively. As  a  check,  this  gives  us  TOLEDO  as 
the  key  word. 

In  the  second  alphabet,  0  is  four  letters  to  the 
left  of  E;  we  may  place  0  four  letters  to  the  left  of 
E  in  the  fourth  and  it  comes  under  V.  Note  that  in 
the  fourth  frequency  table  0  (=V)  does  not  occur. 
In  the  same  way  in  the  fourth  alphabet,  S  is  four 
letters  to  the  right  of  E;  placing  it  in  the  same  posi- 
tion with  respect  to  E  in  the  second  and  sixth,  we 
have  S  under  I.  We  have  already  noted  that  S  prob- 
ably represents  a  vowel  in  these  two  alphabets.  In 
this  way,  we  may  add  D  and  U  to  the  third  alpha- 
bet from  their  position  in  the  fifth  with  respect  to  L 
and  we  may  add  I  and  0  to  the  fifth  from  their  posi- 
tion in  the  third  with  respect  to  L.  In  every  case  we 
check  results  from  the  frequency  tables  and  find 
nothing  unlikely  in  the  results. 

Now  in  the  second  and  sixth,  let  us  try  Q,  D  and 
U  as  D,  N  and  R  respectively.  We  may  add  these 
letters  to  the  third,  fourth  and  fifth  alphabets  by  the 
method  of  observing  the  number  of  letters  to  the 
right  or  left  of  some  letter  already  fixed.  We  now 
add  L  to  the  second,  third,  fourth  and  sixth  from  its 
position  with  reference  to  D  and  U  in  the  fifth.  M 
is  probably  D  in  the  fourth  and  we  may  add  it  to 
each  of  the  alphabets,  except  the  first,  in  the  same 
way.  The  table  is  now  complete  as  shown. 

Let  us  try  these  letters  on  the  first  line  of  the 
message  and  see  if  some  other  letters  will  be  self- 
evident. 

Alphabet  123456123456123456123456123456 
Message  DDLRMERGLMU  J  TLLCHERSLSOEESM  E  JU 
Deciphered  NA  UE  ADE  ABAL  E  IAENE  I GA  R 


—70— 

Referring  to  our  frequency  tables  as  a  check  on 
suppositions,  we  find  everything  agrees  well  enough 
if  we  assume  the  first  line  to  read: 

UNAFUERZA  DE  CABALLERIA  ENEMIGA 

We  will  now  put  the  newly  found  letters  in  the 
table.  The  letters  previously  found  are  in  capitals 
and  the  new  letters  in  small  letters.  The  addition 
of  D  (  =  U)  to  the  first  alphabet  permits  us  to  add  all 
the  letters  of  the  other  alphabets  to  the  first  by  the 
methods  already  discussed.  Each  of  the  other  letters 
may  then  be  added  to  every  alphabet  by  these 
methods: 

ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ 

1st  T        xhgoljqei    msr     d    c  u 

2d  t       xhgOLJQET   Msr    D    c    u 

3d  t      xhgOLJQEi    Msr     D   c   u 

4bh  b        xhgOLJQEi  Msr      D  c  u 

5th          t          XhgOLJQEi     MSr       D   C    U 

6th  t          XhgOLJQEi    MSr      D     C     U 

One  alphabet  checks  another  in  this  way  and  we 
find  everything  to  fit  so  far.  We  will  decipher  a  few 
words  more  of  the  cipher  message  by  the  above  al- 
phabets and  see  if  we  can  determine  some  new  let- 
ters. 

Alphabet 

5612345612345612345612345612345612345612345612345612345612 

Message 

JU  ZJjI  MUDAEE  S  DUTD  BGU  GPN  RCHOB  EQ  E  IEO  OAC  DE  I  OOGC  OL  JL  PDUVM  IGIYXQ 

Deciphered 

PR    CEDEN      EDEARAU UEZ ILLA ECASEHA  _LAENAZUCAICA AB     HEUS     ED 

Again  referring  to  the  frequency  tables  the  first 
word  is  evidently  .  PRQCEDENTE.  We  have  also 
HALLA  and  MARCHEUSTED.  The  letter  B  may 
be  determined  from  another  cipher  group,  JFBSQDLD 
(56123456)  =POSICION.  The  letter  N  may  be  de- 
termined from  BETNDQXUC  (123456123)  =SERRA- 
DERO.  The  letters  F  and  Y  may  be  determined 
from  JCPJOISLYDUASIUPF  (23456123456123456)  = 


—71— 

COMPANIA  PARTIENDO.     The  completed  alpha- 
bets, arranged  as  before,  are: 

ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ 

1st  TYVNXHGOLJQEIZMSRBADFCPU 

2d  TYVNXHGOLJQEIZMSRBADFCPU 

3d  TYVNXHGOLJQEIZMFRBADFCPU 

4th  TYVNXHGOLJQEIZMSRBADFCPU 

5th  TYVNXHGOLJQEIZMSRBADFCPU 

6th  TYVNXHGOLJQEIZMSRBADFCPU 

The  key  word  is  TOLEDO  and  the  completely 
deciphered  message  is: 

"Una  fuerza  de  caballeria  enemiga  procedente 
de  Aranjuez  y  Villaseca  se  halla en  Azucaica.  Marche 
usted  con  su  compania  partiendo  de  la  casa  de  la 
serradero  por  las  alturas  de  lo  este  y  norte  de  Azuca- 
ica con  el  fin  de  reconocer  su  numero  y  clase  de  fuer- 
zas  y  en  disposicion  que  se  halla.  (Q)  Estaacantonada 
(Q)  Se  hallan  otras  tropas  detras  de  ella  (Q).  El  re- 
sultado  del  reconocimiento  necesito  saberlo  dentro 
de  tres  horas  y  media  cuando  mas.  Pongo  a  sus 
ordenes  un  ciclista  (X)  Fin." 

Special  Solution  for  Case  7 

When  a  short  message  is  enciphered  with  a  long 
key  word,  the  methods  of  analysis  already  discussed 
may  fail;  first,  because  there  will  be  no  recurring 
pairs  to  indicate  the  number  of  alphabets  used  and, 
second,  because  there  will  be  so  few  letters  in  each 
alphabet  that  the  methods  of  Case  6  will  not  be  easily 
applied. 

However,  if  we  know  or  correctly  assume  one 
word,  preferably  a  fairly  long  one,  in  the  cipher 
text,  a  solution  is  very  simple.  For  example,  the 
following  message  is  believed  to  refer  to  reenforce- 
ments  and  to  contain  that  word. 

YANZV        ZNLPP        KQFXI        JBPWA 
NRUQP        EPLOM       CCWHM          I 


—72— 

Let  us  assume  that  REINFORCEMENTS  is  the  first 
word  and  that  it  is  represented  by  the  cipher  group 
YANZVZNLPPKQFX.  We  may  put  the  test  in  this 
tabular  form,  using  a  cipher  disk  and  a  Larrabee 
cipher  card  to  determine  the  value  of  A  for  each 
letter  under  these  two  systems.  Any  other  alpha- 
bets suspected  may  be  tried  out  at  the  same  time. 

If 

YANZVZXLPPKQFX 

equals 

REINFORCEMENTS 

then,  with  cipher  disk,  A  equals 

PERMANENTBODYP 

and,  in  Vigenere  cipher,  A  equals 

HWFMQLWJLDGDMF 

It  is  evident  that  the  guess  as  to  the  appearance 
of  the  word  REINFORCEMENTS  was  correct,  that 
it  is  the  first  word  of  the  message,  that  the  cipher 
disk  was  used  in  preparing  the  cipher  and  that  the 
key  words  are  PERMANENT  BODY. 

This  is,  of  course,  an  especially  favorable  case 
and  we  will  take  one  less  favorable  to  show  how 
this  method  can  be  applied. 

Two  Mexican  chieftains,  A  and  B,  have  been 
communicating  with  the  following  cipher  alphabet: 

Plain  text        ABCDEFGHIJLMNOPQRSTUVXYZ 
Cipher  PCJVRQZBAODFSUTMXIYHLGEN 

This  alphabet  has  been  determined  from  many 
radio  messages  from  A,  the  superior,  to  B,  his  sub- 
ordinate, who  has  a  force  of  about  2,000  men  near 
the  border.  A  uses  the  form  ORDENO  QUE  instead 
of  the  more  familiar  MANDO  QUE  in  all  his 
messages  giving  orders  to  B.  The  following 
message  is  received  from  A  by  B's  radio  station 
(and  other  listening  stations)  and  about  an  hour 


—73— 

later  there  is  a  good  deal  of  noise  and  movement  as 
if  B's  force  were  breaking  camp. 

IIHAH          YDXRP        EGQGV        JJEEE        HOBGV 
GJCAG         XAESA        VVXLE        IILHM        PSQAG 
BDGAV        GSQAZ 

This  is  a  substitution  cipher,  but  it  is  not  Case  6 
using  the  usual  alphabet  of  the  communications  from 
A  to  B  and,  in  fact,  is  not  Case  6  at  all.  The  re- 
curring pairs  and  triplets  point  to  a  key  word  of  ten 
letters  and  this  would  give  us  but  six  letters  per 
alphabet  if  it  is  Case  7. 

The  preparations  for  a  move  lead  us  to  believe 
that  A  has  given  an  order  to  B  and  he  has,  in  that 
case,  probably  used  the  expression  ORDENO  QUE 
in  the  message.  We  will  try  the  first  nine  letters  of 
the  message  as  in  the  other  example,  first  preparing 
a  cipher  disk  or  equivalent  sliding  arrangement  hav- 
ing on  it  the  alphabet  usually  used  between  these 
chieftains  or  A-B  cipher. 

Fixed  Cipher  Alphabet 

PCJVRQZBAODFSUTMXIYHLGENPCJVRQZBAODFSUTMXIYHLGEN 


ABCDEFGHIJLMNOPQRSTUVXYZ 

Sliding  Plain  Text  Alphabet 


A-B  Cipher 

If  I  equals  O  then  A  equals  R 

I                 R  C 

H                D  -X 

A                 E  R 

H                 N  B 

Y                  O  Q 

Clearly  there  is  nothing  here  and  the  assumed 
words,  if  they  occur,  are  in  the  middle  of  the  mes- 
sage. We  may  jump  to.  the  combination  PEGQGV 
at  once  since  the  preceding  letters  do  not  make 
ORDENO  QUE.  We  try  this  without  result  and 
proceed  to  EGQGVJ,  GQGVJJ,  QGVJJE,  GVJJEE, 


—74— 

VJJEEE,  JJEEEH,  JEEEHO,  EEEHOB,  EEHOBG, 
EHOBGV,  HOBGVG,  OBGVGJ,  BGVGJC,  GVGJCA, 
VGJCAG,  all  without  result.  This  work  requires  less 
time  than  might  be  imagined  and  is  the  kind  of  work 
which  can  be  divided  among  a  number  of  operators. 
Now  let  us  come  to  the  next  combination  GJCAGX. 
We  add  the  next  three  letters,  AES,  against  QUE. 

If 

G  JC  AGX     AES 

equals 

ORDENO    QUE 
Then,  in  the  A-B 
cipher,  A  equals 

ADEROV    IVA 

The  key  is  found;  VIVA  ADERO  and  a  trial  of  M 
in  the  blank  space  shows  correct  results.  .  This 
checks  with  our  theory  that  a  ten  letter  key  word 
was  used  and  deciphering  the  message  we 
have: 

PARA    EL    ATAQUE    CONTRA     TORREON     ORDENO     QUE     SUS 
TROPAS  MARCHEN  ESTE  NOCHE    X. 

The  reason  for  breaking  camp  is  now  evident. 

This  method  may  be  used,  with  some  labor,  on 
short  words  like  THE,  AND,  etc.  Parts  of  the  key 
will  appear  whenever  an  assumed  word  is  found  in 
the  message  and  the  whole  key  may  be  assembled  if 
enough  of  the  parts  are  available.  Even  if  only  part 
of  the  key  may  be  so  recovered,  it  will  always  lead 
to  the  ultimate  solution  of  the  cipher  by  trial  of  the 
partially  recovered  key  on  the  message  letter  by 
letter. 

As  an  example  of  recovery  of  a  key  by  use  of 
short  'common  words,  let  us  refer  to  the  message  of 
Case  7-a.  There  are  twenty-four  groups  of  three 
letters  each  in  this  message  and  we  will  try  them 
against  THE,  ARE  and  YOU,  assuming  that  the 
Vigenere  cipher  is  used. 


—75— 

12         3          4567         8         9       10       11      12 
If  OSB  VOI  GSW   CYY  ZSZ  BVJ  XLD   OSY  UVD   YJL  SQA  HSI 

equals  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE 

Or      ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE 
Or     YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU 

then  A 

equals  VJLX  CHE  NLS  JRU  GLV  IOP  EEZ  VLU  BOZ  FCH  zjw  OLE 

Or  OBX  VXE   GBS  CHU  ZBV  BEF  XUZ  OBU  UEZ  YSH  SZW  HBE 

Or  QEH  XAO  IEC  EKE  BEF  DHP  ZXJ  QBE  WHJ  AYR  UCG    JEO 

13     14       15      16      17     18       19      20       21       22       23      24 
If  BJV  SFX  DQB    AH  OHZ  IVX    JBF  ESF    JSC    NLU  CTW  CSM 

equals  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE 

Or     ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE 
Or     YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU 

then  A 

equals  ICR  ZYT  KJX  HBE  VAV  POT  QUB  LLB  OJLY  UEQ  JMS  JLI 

Or  BSR   SOT  DZX  ARE    OQV  IET  JKB  EBB  JBY     NUQ  CCS  CBI 

Or  DVB  URD  FCH  YUO  QTF  KHD  LNL  GEL  LEI     PXA   EFC   EES 

In  column  5,  we  have,  for  YOU,  the  key  BEF; 
column  6  gives  the  same  key  for  ARE;  column  10 
gives  the  key  FCH  for  THE  and  column  15  gives  the 
same  key  for  YOU;  column  12  gives  the  key  HBE  for 
ARE  and  column  16  gives  the  same  key  for  THE; 
column  23  gives  the  key  EFC  for  YOU.  The  only 
possible  key  for  the  message  is  a  five-letter  one  made 
up  of  the  letters  BEFCH  or  EFCHB  or  FCHBE  or 
CHBEF  or  HBEFC.  If  the  key  in  this  case  were  a 
word,  we  would  have  no  difficulty  in  determining  it; 
as  it  is,  there  is  no  real  difficulty  in  the  matter  as  we 
may  now  divide  the  message  into  blocks  of  five  let- 
ters and  note  that  ZSZ  (  =  YOU)  form  the  3d,  4th  and 
5th  letters  of  a  group.  The  corresponding  key  let- 
ters, BEF,  are  then  the  3d,  4th  and  5th  letters  of  the 
key  which  must  be  CHBEF. 

This  special  solution  for  Case  7  depends  so  largely 
on  the  intuition  of  the  operator  in  choice  of  a  word 
that  it  is  not,  in  general,  advisable  to  use  it  unless  the 
message  is  very  short  and  the  regular  methods  of 
analysis  have  been  tried  unsuccessfully.  It  is,  how- 
ever, a  wonderfully  short  cut  in  difficult  cases  where 
the  other  methods  fail. 


Chapter  VIII 


GASE  8.  The  Play  fair  cipher.  This  is  the  Eng- 
lish military  field  cipher;  as  the  method  is  pub- 
lished in  English  military  manuals  and  as  it  is  a  cipher 
of  proven  reliability,  it  may  be  met  with  in  general 
cipher  work.  The  Playfair  cipher  operates  with  a 
key  word;  two  letters  are  substituted  for  each  two 
letters  of  the  text. 

The  Playfair  cipher  may  be  recognized  by  the 
following  points:  (a)  It  is  a  substitution  cipher, 
(b)  it  always  contains  an  even  number  of  letters,  (c) 
when  the  cipher  is  divided  into  groups  of  two  letters 
each,  no  group  consists  of  the  repetition  of  the  same 
letter  as  SS  or  BB,  (d)  there  will  be  recurrence  of 
pairs  throughout  the  message,  following  in  a  general 
way,  the  frequency  table  of  digraphs  of  pairs,  (e) 
in  short  messages  there  may  be  recurrence  of  cipher 
groups  representing  words  or  even  phrases,  and  these 
will  always  be  found  in  long  messages. 

In  preparing  a  cipher  by  this  method,  a  key 
word  is  chosen  by  the  correspondents.  A  large  square, 
divided  into  twenty-five  smaller  squares,  is  constructed 
as  shown  below  and  the  letters  of  the  key  word  are 
written  in,  beginning  at  the  upper  left  hand  corner. 
If  any  letter  recurs  in  the  key  word,  it  is  only  used 
on  the  first  occurrence.  The  remaining  letters  of 
the  alphabet  are  used  to  fill  up  the  square.  It  is 
customary  to  consider  I  and  J  as  one  letter  in  this 
cipher  and  they  are  written  together  in  the  same 
square. 

If  the  key  word  chosen  is  LEAVENWORTH, 
then  the  square  would  be  constructed  as  follows: 

76 


—77— 


L 

E 

A 

V 

N 

W 

O 

R 

T 

H 

B 

C 

D 

F     G 

IJ 

K 

M 

P  |Q 

ti 

U 

X 

Y 

Z 

The  text  of  the  message  to  be  sent  is  then  divided 
up  into  groups  of  two  letters  each,  and  equivalents 
are  found  for  each  pair. 

Every  pair  of  letters  in  the  square  must  be: 
Either  (1)  in  the  same  vertical  line.  Thus  in  the 
above  example  each  letter  is  represented  in  cipher 
by  that  which  stands  next  below  it,  and  the  bottom 
letter  by  the  top  one  of  the  same  column;  for  instance, 
TY  is  represented  by  FV. 

Or  (2)  in  the  same  horizontal  line.  Each  letter 
in  this  case  is  represented  by  that  which  stands  next 
on  its  right,  and  the  letter  on  the  extreme  right  by 
that  on  the  extreme  left  of  the  same  horizontal  line 
with  it;  for  instance  RH  is  represented  by  TW. 

Or  (3)  at  opposite  corners  of  a  rectangle.  Each 
letter  of  the  pair  is  represented  by  the  letter  in  the 
other  corner  of  the  rectangle  in  the  same  horizontal 
line  with  it;  for  instance  TS  is  represented  by  WY. 

If,  on  dividing  the  letters  of  the  text  into  pairs, 
it  is  found  that  a  pair  consists  of  the  same  letter  re- 
peated, a  dummy  letter,  as  X,  Y,  or  Z,  should  be  in- 
troduced to  separate  the  similar  letters. 

If  the  message  to  be  sent  were  "The  enemy 
moves  at  dawn,"  it  would  be  divided  into  pairs: 

TH  EX  EN  EM  YM  OV  ES  AT  DA  WN 
and  enciphered:  HWAU  AL  AK  XP  TE  LU  VR  MR  HL 

The  message  is  then  broken  up  into  groups  of 
five  letters  for  transmission. 

To  decipher  such  a  cryptogram,  (knowing  the 
key  word),  the  receiver  divides  it  into  pairs,  and 


—78— 

from  his  table  finds  the  equivalent  of  these  pairs, 
taking  the  letter  immediately  above  each,  when  they 
are  in  the  same  vertical  line;  those  immediately  on 
the  left,  when  in  the  same  horizontal  line;  and  those 
at  opposite  angles  of  the  rectangle  when  this  is 
formed. 

It  is  evident,  from  the  foregoing  description, 
that  any  letter  of  the  plain  text  may  be  represented 
in  cipher  by  one  of  five  letters,  viz:  The  one  next 
below  it  and  the  other  four  letters  in  the  same  hori- 
zontal line  with  it  in  the  square.  Take,  for  example, 
the  letter  D  of  the  plain  text,  in  combination  with 
each  of  the  other  letters  of  the  alphabet.  We  have, 
using  the  key  LEAVENWORTH: 

DA  DB  DC  DK  DP  DG  DH  DI  DK  DL  DM  DN  DO  DP  DQ  DK  DS  DT  DU  DV  DW  DX  DY  DZ 
MR  PC  FD  CA  PG  PB  GR  BM  CM  BA  MX  GA  CR  FM  GM  MD  BX  PR  CX  PA  BR  MA  FX  GX 

This  gives  D  represented  by     B  C  F  G  M 

44844    times, 

and,  connected  with  these  five  letters  representing  D, 
we  have  ARDMXBCG 

55245111     times. 

Note  that  these  letters  are  those  of  the  vertical 
column  containing  D  plus  the  letters  B,  C  and  G,  of 
the  horizontal  line  containing  D. 

Lieut.  Frank  Moorman,  U.  S.  Army,  has  de- 
veloped a  method  for  determining  the  letters  which 
make  up  the  key  word  in  a  Playfair  cipher.  In  the 
first  place,  a  key  word  necessarily  contains  vowels  in 
the  approximate  proportion  of  two  vowels  to  three 
consonants  and  it  is  also  likely  that  a  key  word  will 
contain  other  common  letters.  This  key  word  is 
placed  in  the  first  row  or  rows.  Now  if  a  table  is 
made,  showing  what  letters  in  the  cipher  occur  with 
every  letter,  it  will  be  found  that  the  letters  having 
the  greatest  number  of  other  letters  in  combination 
with  them  are  very  likely  to  be  letters  of  the  key 


—79- 
word,  or  in  other  words,  letters  occurring  in  the  first 
or  second  lines.     An  example  will  make  this  clear: 

Message 

DB  FN  EX  TZ  MF  TO  VB  QB  QT  OB  XA  OF  PR  TZ  EQ 
BH  QK  QV  DX  OK  AB  PR  QI  EL  TV  KE  EX  XS  FS  BP 
WD  BO  BY  BF  RO  EA  BO  RH  QK  QV  TX  GU  EL  AB  TH 
TR  XN  ON  EA  AY  XH  BO  HN  EX  BS  HR  QB  ZM  SE  XP 
HF  GZ  UG  KC  BD  PO  EA  AY  XH  BO  XP  HF  KR  QI  AB 
PR  QI  EL  BX  FZ  BI  SE  FX  PB  RA  PR  QI  WC  BR  XD 
YG  TB  QT  EA  AY  XH  BO  HN  EX  BS  HR  QB  PR  QI  EL 
BX  BT  HB  QB  NF  SI  SE  BX  NU  XP  BU  RB  XB  QR  OX 
BA  TB  RH  BP  WD  RP  RO  GU  GX  QR  SE  ZY  OX  BA  EL 
AX  CW  BY  BA  SX  RK  RO  PR  HB  OP  BD  PI  CN  OX  EM 
RP  KR  XT  EL  AXCWEQ  FZ  SX  EL  RH  RO  PR  HB  UX 
DA  SE  XN  ZN  GU  EL  BX  FS  DG  DB  TB  ZL  VE  RH  BO 
RQ. 

From  this  message,  we  make  up  the  following 
table,  considering  the  letters  of  each  pair: 


(Table  on  next  page.) 


—80— 
First  Letters  of  Pairs 


A 

B 

C 

D 

E 

F 

Q 

H 

I 

K 

L 

M 

N 

O 

P 

Q 

R 

S 

T 

U 

V 

w 

X 
Y 
Z 


A|B 

C 

D 

E 

F 

G 

H 

I 

K 

L 

M 

N 

0 

P 

Q 

R 

S 

T 

U 

V 

w 

X 

Y 

Z 

3 

1 

4 

1 

1 

3 

2 

3 

1 

1 

4 

1 

3 

1 

1 

1 

1 

2 

2 

1 

1 

5 

1 

1 

2 

1 

1 

1 

1 

1 

1 

1 

I 

5 

1 

3 

1 

1 

5 

1 

I 

1 

2 

1 

1 

8 

1 

1 

1 

| 

1 

1 

2 

1 

2 

1 

6 

1 

4 

1 

2 

1 

2 

3 

2 

1 

2 

2 

7 

2 

1 

2 

2 

1 

1 

2 

1 

1 

3 

1 

2 

2 

1    5 

1 

4 

1 

1 

3 

2 

1 

1 

5 

1 

2 

1 

2 

From  this  table  we  pick  out  the  letters  B,  E,  F, 
0,  R,  T,  X,  as  tentative  letters  of  the  key  word  on 
account  of  the  variety  of  other  letters  with  which 
they  occur.  As  there  are  but  two  vowels  for  seven 
letters,  we  will  add  A  to  the  list  on  account  of  its 
occurrences  with  B,  D,  E,  R,  and  X.  This  leaves 
the  letters  for  the  bottom  lines  of  the  square  as  fol- 
lows: 


—81— 


— 

— 

— 

C     D 

G 

H 

IJ 

K 

L 

M 

N 

P 

Q 

S 

U 

V 

w 

Y 

z 

Referring  to  the  table  again  we  find  the  most 
frequent  combination  to  be  EL,  occurring  8  times, 
with  no  occurrence  of  LE.  Now,  TH  is  the  com- 
monest pair  in  plain  text,  and  HT  is  not  common. 
The  fact  that  H  occurs  in  the  same  horizontal  line 
with  L  and  that  E  and  T  are  probably  in  the  key, 
will  lead  us  to  put  E  in  the  first  line  over  H  and  T  in 
the  first  line  over  L,  so  as  to  make  EL  equal  TH. 

The  next  most  frequent  combination  is  PR  oc- 
curring 7  times,  with  RP  occurring  twice.  In  the 
square  as  partially  arranged,  PR  equals  M_or  N_or 
Q_or  I_.  We  may  eliminate  all  these  except  N_, 
and  this  N_  could  only  be  NO  or  NA,  so  that  we  will 
put,  tentatively  the  R  in  the  second  line  over  H  and 
the  0  and  A  in  the  same  line  over  IJ.  We  have  then: 


E 

• 

• 

T 

• 

R 

AO 

o 

D 

G 

H 

IJ 

K 

L 

M 

N 

P 

Q 

S 

U 

V 

W 

Y 

Z 

i 

Let  us  now  check  this  by  picking  out  the  combi- 
nations beginning  with  EL  and  seeing  if  the  table 
will  solve  them.  We  find,  ELTV,  ELAB,  ELBXFZ, 
ELBXBT,  ELAXCWBY,  ELAXCWEQ,  ELRH,  ELB- 
XFS.  Now,  on  the  assumption  that  the  letter  after 
EL  represents  E,  we  have  it  represented  by  A  three 
times,  B  three  times,  R  once  and  T  once.  This  re- 


—82— 

quires  that  A  and  B  be  put  in  the  same  horizontal 
line  with  E,  since  T  is  already  there,  and  R  is  tenta- 
tively under  E. 

The  combination  ELTV  now  equals  THEZ.  If 
the  T  were  moved  one  place  to  the  left,  it  would  be 
THEY,  a  more  likely  combination,  but  this  requires 
the  L  to  be  moved  one  place  to  the  left  also,  by  put- 
ting I  or  K  in  the  key  word  and  taking  out  0,  R  or 
X  and  returning  it  to  its  place  in  the  alphabetical 
sequence.  The  most  frequent  pairs  containing  0  are 
B  0  six  times,  R  0  four  times,  and  0  X  three  times. 
Now  these  pairs  equal  respectively  E  N,  E  S  and  H  E, 
if  0  is  put  between  N  and  P  in  the  fourth  line.  We 
will  therefore  cease  to  consider  it  as  a  letter  of  the 
the  key  word.  The  combination  ELAB  can  only  be 
THE  on  the  assumption  that  A  is  the  first  letter  to 
the  right  of  E.  The  combination  ELBX  occurs  three 
times.  If  it  represents  THE  ,  the  B  must  be  the 
first  letter  of  the  first  line  and  the  X  must  now  be 
placed  under  E  where  the  R  was  tentatively  put.  We 
can  get  THE  out  of  ELRH  by  putting  R  in  the  first 
line  or  leaving  it  where  it  is,  but  the  preponderance 
of  the  BX  combination  should  suggest  the  former 
alternative. 

A  new  square  showing  these  changes  will  look 
like  this: 


B 

E 

A 

T 

R 

X 

.. 

. 

G 

H 

L 

M 

N 

O 

P 

Q 

S 

U 

V 

W 

Y 

X 

As  I  put  in  the  space  under  B  will  give  the  word 
BEATRIX  and  as  a  vowel  is  clearly  necessary  there, 
we  will  so  use  the  IJ  and  leave  K  between  H  and  L. 
This  leaves  C,  D  and  F  to  be  placed.  It  appeared  at 


—83— 

first  that  F  was  in  the  key  but  if  it  is  in  the  second 
line,  in  proximity  to  the  letters  of  the  first  line,  it 
will  give  the  same  indications.  Completing  the 
square  then,  we  have 


B 

E 

A 

T 

R 

IJ 

X 

C 

D 

F 

G 

H 

K 

L 

M 

N 

O 

P 

Q 

S 

U 

V 

W 

Y 

z 

With  this  square,  the  message  is  deciphered 
without  difficulty. 

"It  is  very  frequently  neces(x)sary  to  employ 
ciphers  and  they  have  for  many  centuries  been  em- 
ployed in  the  relations  betwe(x)en  governments,  for 
com(x)munication  betwe(x)en  com(x)manders  and 
their  subordinates  and  particularly  betwe(x)en  gov- 
ernments and  their  agents  in  foreign  countries; 
there  are  many  cases  in  history  where  the  capture  of 
a  message  not  in  cipher  has  made  the  captors  of  the 
message  victorious  in  their  military  movements. " 

It  will  be  seen  that  the  method  of  Lieut.  Moor- 
man enabled  us  to  pick  out  six  letters  of  the  key 
word  out  of  eight  letters  chosen  tentatively.  The 
reason  for  the  appearance  of  F  has  already  been 
noted;  the  letter  0  occurred  with  many  other  letters 
because  it  happened  to  remain  in  the  same  line  with 
N  and  S  and  to  be  under  H.  It  thus  was  likely  to 
represent  any  of  these  three  letters  which  occur 
very  frequently  in  any  text. 

Two-character   Substitution   Ciphers 

CASE  9.  —Two-character  substitution  ciphers.  In 
ciphers  of  this  type,  two  letters,  numerals,  or  con- 
ventional signs,  are  substituted  for  each  letter  of  the 
text.  There  are  many  ways  of  obtaining  the  char- 


—84— 

acters  to  be  substituted  but,  in  general,  these  ciph- 
ers may  be  considered  as  special  varieties  of  Case  6 
or  Case  7.  The  ciphers  which  come  under  this  case 
are  not  well  suited  to  telegraphic  correspondence  be- 
cause the  cipher  message  will  contain  twice 
as  many  letters  as  the  plain  text.  However  they 
are  so  used;  an  example  is  at  hand  in  which  two 
numerals  are  substituted  for  each  letter  and  this 
makes  transmission  by  telegraph  very  slow. 

Case  9  can  be  recognized  by  some  or  all  of  the 
following  points;  the  number  of  characters  in  the 
cipher  is  always  an  even  number;  of  ten  only  a  few, 
say  five  to  ten,  of  the  letters  of  the  alphabet  appear; 
either  a  frequency  table  for  pairs  of  the  cipher  text 
resembling  the  normal  single  letter  frequency  table 
can  be  made,  or  groups  of  four  letters  will  show  a 
regular  recurrence,  from  which  the  cipher  can  be 
solved  as  in  Case  7. 

CASE9a.— 

Message 


RNTGN 
RARAT 
NRNAA 
TGGRN 

NNARN 
NGNAT 

RAAGR 
NAANR 
AANRA 
ARNTG 
ARNRT 
NNNAT  : 

NARNA 

NNNRN 
TNANN 
NNART 
TGAGG 

GTGRA 
AAAGG 
NGGRN 
GGRNR 
GAAAA 

TGAAN 
AANGR 
RNNRG 
GRNNT 

NANNA 

NANGG 
NGGNN 
TTGRG 
GTGAA 
RNAGA 

This  message  contains  160  letters  and  it  will  be 
noted  that  the  only  letters  used  are  A,  G,  N,  R  and 
T. 

We  may  expect  a  simple  two-letter  substitution 
cipher  at  once.  -It  will  simplify  the  work  if  we  di- 
vide the  cipher  into  groups  of  two  letters  and  then, 
if  we  find  there  are  26  or  less  recurring  groups,  to 
assign  an  arbitrary  letter  to  each  group  and  work 
out  the  cipher  by  the  method  of  Case  6. 

RN  TG  NR  AA  GR  NA  RN  AG  TG  RA  TG  AA  NN  AN  GG 

RA  RA  TN  AA  NR  NN  NR  NA  AA  GG  AA  NG  RN  GG  NN 

NR  NA  AA  AN  RA  TN  AN  NN  GG  RN  RN  NR  GT  TG  RG 

TG  GR  NA  RN  TG  NN  AR  TG  GR  NR  GR  NN  TG  TG  AA 

NN  AR  NA  RN  RT  TG  AG  GG  AA  AA  NA  NN  AR  NA  GA 

NG  NA  TN  NN  AT 


—85— 
With  arbitrary  letters  substituted,  we  have 

ABCDEFAGBHBDIJK 
HHLDCI  CFDKDMAKI 
CFDJ  HL  J  IKAA  CNBO 
BEFABIPBECE  BED 

I  PFA  QBGKDDF  IPFR 
M  F  L  I  S 

Now,  preparing  a  frequency  table,  with  note  of 
prefixes  and  suffixes  we  have: 

Frequency  Prefix  Suffix 

A      1     1111111  FMKAFF  BGKACBQ 

B   10    1111111111  AGHNOAPIBQ  CHDOE1EBDG 

C      6     111111  BDIIAE  DIFFNE 

D     9    111111111  CBLFKFBKD  EICKMJIDF 

E      4     1111  DBBC  FFCI 

F     8    11111111  ECCEPDPM  ADDAAIBL 

G     2     11  AB  BK 

H     4    1111  BKJH  BHLL 

I       9    111111111  DCKJBEDFL  JCCKPBPP 

J      3    111  IDL  KHI 

K      5    11111  JDAIG  HDIAD 

L      3    111  HHF  DJI 

M     2     11  DR  AF 

Nil  C  B 

Oil  B  B 

P      3    111  III  BFF 

Q      1     1  A  B 

R     1    1  F  M 

S      1     1  I 

A  brief  study  of  this  table  and  the  distribution 
in  the  cipher  leads  to  the  conclusion  that  B,  F  and  C 
are  certainly  vowels  and  are,  if  the  normal  frequency 
holds,  equal  to  E,  0,  and  A  or  I.  Similarly  D  and  I 
are  consonants  and  we  may  take  them  as  N  and  T. 
I  is  taken  as  T  because  of  the  combination  IP  (=  pos- 
sibly TH)  occurring  three  times.  The  next  letter  in 
order  of  frequency  is  A;  it  is  certainly  a  consonant 
and  may  be  taken  as  R  on  the  basis  of  its  frequency. 
Let  us  now  try  these  assumptions  on  the  first  two 
lines  of  the  message.  We  have 


This  is  clearly  the  word  REINFORCEMENTS 
and,  using  the  letters  thus  found,  the  rest  of  the  line 
becomes  AMMUNITIONAND.  We  have  then  the 
following  letters  determined: 

Arbitrary  letters    ABCDEFGHIJKLM 
Plain  Text  RE  I  NFOCMTSAUD 


—86— 
If  these  be  substituted  we  have  for  the  message: 

REINFORCEMENTS  AMMUNITION  AND  RATIONS  MUST 


ARRI_E_EFORE   T 
O    D  OUT     , 


E   FIFTEENT       OR       E    CANNOT 


From  this  the  remainder  of  the  letters  are  de- 
termined: 

Arbitrary  letters    N  O  P  Q  R  S 
Plaintext  VBHWLX 

Now  let  us  substitute  the  two-letter  groups  for 
the  arbitrary  letters: 

Arbitrary  letters     KOGMBEPCRHDFAJ1LNQS 
Two-letter  groups  GGRGAGNGTGGRARNRGARAAANARXANNNTNGT  RT  AT 

Plain  text  AB.CDEFHILMNORSTUVWX 

It  is  evident  that  the  cipher  was  prepared  with 
the  letters  of  the  word  GRANT  chosen  by  means  of 
a  square  of  this  kind: 

GRANT 
G  A  B  C  D  E 
R  F  G  H  I  K 
A  L  M  N  O  P 
N  Q  R  S  T  U 
T  V  W  X  Y  Z 

Thus  TG  — E,  AN  =  S,  etc.,  as  we  have  already 
found. 

CASE  9-b 

Message 

1950492958  3123252815  4418452815  2048115041 

2252115345  5849134124  5028552526  5933195222 

5245113215  6215584143  2861361265  2945565015 

2342455850  6345542019  1550185311  2115415828 

1124174553  4554205950  2552454132  1533492048 
5018152364 

An  examination  of  the  groups  of  two  numerals 
each  which  make  up  this  message,  shows  that  we 
have  11  to  36  and  41  to  65  with  eleven  groups  missing. 
Now  the  11  to  36  combination  is  a  very  familiar  one 
in  numeral  substitution  ciphers  (See  Case  6-c)  and  it 


—87— 

will  be  noted  that  41  to  66  would  give  us  a  similar 
alphabet.  Let  us  make  a  frequency  table  in  this 
form: 


Group  Frequency 

11 

11J11 

12 

1 

13 

1 

14 

15 

111111111 

16 

17 

1 

18 

111 

19 

111 

20 

1111 

21 

1 

22 

11 

23 

111 

24 

11 

25 

111 

26 

1 

27 

28 

11111 

29 

11 

30 

31 

1 

32 

11 

33 

11 

34 

35 

36 

1 

Group 

Frequency 

41 

11111 

42 

1 

43 

1 

44 

1 

45 

111111111 

46 

47 

48 

11 

49 

111 

50 

11111111 

51 

52 

1111 

53 

111 

54 

11 

55 

1 

56 

1 

57 

58 

11111 

59, 

11 

60 

61 

1 

62 

1 

63 

1 

64 

1 

65 

1 

66 

Each  of  these  tables  looks  like  the  normal  fre- 
quency table  except  for  the  position  of  20  and  50 
which  should  represent  T,  by  all  our  rules,  and  should 
be  apparently  30  and  60.  But  suppose  we  put  the 
alphabet  and  corresponding  numerals  in  this  form: 

1234567890 
Ior4     ABCDEFGHIJ 

2  or  5  KLMNOPQRST 

3  or  6  UVWXYZ 


—88— 

Then  A  ^11  or  41,  J  =  10  or  40  and  T=20  or  50 
as  we  found.  Using  the  above  alphabet,  the  mes- 
sage may  easily  be  read.  Note  that  this  cipher  is 
made  up  of  ten  characters  only,  the  Arabic  numerals. 

CASE  9c— 


1156254676 
4924213511 
4055461512 
2514764553 
4952197929 
4551491411 

2542294432 
7424147875 
7573227945 
1548342126 
7015242143 
7321171554 

Message 

1949294015 
7646252444 
1627481511 
7215254075 
2925444933 

1423217211 
5143254845 
7042351944 
1611257845 
1970187531 

2979703115 
3179742533 
1378252149 
4642217415 
4079254829 

An  examination  of  this  message  shows  it  to  con- 
sist of  forty-four  different  two-figure  groups  run- 
ning from  11  to  79.  Let  us  prepare  a  frequency 
table  of  these  groups. 


Group 

Frequency 

Group 

Frequency 

11 

111111 

31 

111 

12 

1 

32 

1 

13 

1 

33 

11 

14 

1111 

34 

1 

15 

111111111 

35 

11 

16 

11 

36 

17 

1 

37 

18 

1 

38 

19 

1111 

39 

20 

40 

1111 

21 

1111111 

41 

22 

1 

42 

111 

23 

1 

43 

11 

24 

1111 

44 

1111 

25 

11111111111 

45 

11111 

26 

1 

46 

1111 

27 

1 

47 

28 

48 

1111 

29 

111111 

49 

111111 

30 

50 

Group 

Frequency 

51 

11 

52 

1 

53 

1 

54 

1 

55 

1 

56 

1 

57 

58 

59 

70 

1111 

71 

72 

11 

73 

11 

74 

111 

75 

1111 

76 

111 

77 

78 

111 

79 

11111 

We  at  once  note  the   resemblance   between   the 
frequency  tables  for  the  groups  11  to   19  and   21   to 


—89— 

29;  for  the  groups  30  to  36  and  50  to  56;  and  for  the 
groups  40  to  49  and  70  to  79.  Also  the  groups  11  to 
19  and  21  to  29  have  a  frequency  fitting  well  with  the 
normal  frequency  table  of  the  letters  A  to  I;  the 
groups  41  to  49  and  71  to  79  have  a  frequency  fitting 
well  with  the  normal  frequency  table  of  the  letters 
K  to  S;  and  the  groups  31  to  36  and  51  to  56  have  a 
frequency  fitting  well  with  the  normal  frequency 
table  of  the  letters  U  to  Z.  We  have  J  and  T  un- 
accounted for,  but  note  what  occurred  in  Case  9-b 
and  that  40  and  70  would  correspond  well  with  T  if 
they  followed  respectively  49  and  79.  We  may  now 
make  up  a  cipher  table  as  follows. 

1234567890 
Ior2  ABCDEFGHIJ 
4  or  7  KLMNOPQ.  RST 
3  or  5  UVWXYZ 

and  this  table  will  solve  the  cipher  message. 

In  ciphers  coming  under  case  9-b  and  9-c,  it  is 
not  uncommon  to  assign  some  of  the  unused  numbers 
such  as  85,  93,  etc. ,  to  whole  words  in  common  use  or 
to  names  of  persons  or  places.  In  case  such  groups 
are  found,  the  meaning  must  be  guessed  at  from  the 
context;  but  if  many  messages  in  the  same  cipher 
are  available,  the  meaning  of  these  groups  will  soon 
be  obtained.  The  appearance  of  such  odd  groups  of 
figures  in  a  message  does  not  interfere  materially 
with  the  analysis,  and  it  will  be  apparent  at  once  on 
deciphering  the  message  that  they  represent  whole 
words  instead  of  letters. 


Chapter  IX 

Other  Substitution  Methods 

The  foregoing  cases  by  no  means  exhaust  the 
possibilities  of  the  substitution  cipher  but  they  cover 
practically  all  methods  which  are  satisfactory  for 
military  purposes,  having  in  mind  conservation  of 
time,  the  minimizing  of  mental  strain,  and  the  re- 
quirements that  complicated  apparatus  and  rules  be 
avoided,  and  that  the  resulting  cipher  should  be 
adapted  to  telegraphic  correspondence. 

A  message  may  be  re-enciphered  two  or  more 
times  using  a  different  key  word  each  time  or  it  may 
be  enciphered  by  one  method  and  re-enciphered  by 
another  method,  using  the  same  or  a  different  key 
word.  Complicated  cipher  systems  requiring  the 
memorizing  of,  or  reference  to,  numerous  rules  have 
been  devised  for  special  purposes.  Such  systems 
usually  fail  utterly  if  there  are  any  errors  in  trans- 
mission and  it  will  be  seen  later  that  such  errors  are 
very  common. 

There  are  several  ingenious  cipher  machines  by 
which  complicated  ciphers  can  be  formed,  but  if  the 
apparatus  is  available  and  fairly  long  messages  are 
at  hand  for  examination,  it  is  usually  possible  to 
solve  them.  Such  machines  are  not,  as  a  rule, 
simple  and  small  enough  for  field  use;  and  it  must 
always  be  remembered  that  a  machine  cipher  oper- 
ates on  certain  mechanical  cycles,  which  can  be  de- 
termined if  the  machine  is  available. 

A  book  by  Commandant  Bazeries,  entitled  "Etude 
sur  la  Cryptographic  Militaire,"  and  a  series  of 
90 


—91— 

articles  by  A.  Collon,  entitled  '  'Etude  sur  la  Crypto- 
graphic," which  appeared  in  the  Revue  de  L'Armee 
Beige,  1899-1902,  give  illustrations  and  details  of 
operation  of  several  of  these  cipher  machines  and 
the  latter  goes  into  the  methods  of  deciphering  mes- 
sages enciphered  with  them.  These  methods  of  analy- 
sis require  long  messages,  and  as  each  one  is  adapted 
only  to  the  product  of  a  certain  machine  or  apparatus, 
it  is  not  considered  advisable  to  include  a  discussion 
of  them  here.  Those  interested  in  such  advanced 
cipher  work  must  refer  to  these  and  other  European 
authors  on  the  subject. 

The  requirement  that  cipher  messages  should  be 
adapted  to  telegraphic  transmission,  practically  ex- 
cludes ciphers  in  which  three  or  more  letters  or 
whole  words  are  substituted  for  each  letter  of  the 
plain  text.  Such  ciphers  might  be  used  for  the 
transmission  of  very  short  messages  but  in  no  other 
case. 

The  cipher  of  Case  7,  with  a  key  .word  or  phrase 
longer  than  one-fourth  of  the  message,  the  cipher 
after  the  method  of  Case  7,  using  a  certain  page  of 
a  book  as  a  key,  and  the  cipher  with  a  running  key, 
where  each  letter  of  the  cipher  is  the  key  for  en- 
ciphering the  next  letter,  all  look  safe  and  desirable, 
theoretically,  but,  practically,  the  work  of  encipher- 
ing and  deciphering  is  hopelessly  slow,  and  errors  in 
enciphering  or  transmission  make  deciphering  very 
difficult.  Incidentally  the  first  and  second  of  these 
ciphers  can  be  solved  by  the  special  solution  for 
Case  7,  and  the  third  can  be  solved  by  trying  each  of 
the  twenty-six  letters  of  the  alphabet  as  the  first  key 
letter,  and  then  continuing  the  work  for  five  or  six 
letters  of  the  cipher.  When  the  proper  primary  key 
letter  is  found,  the  solution  of  the  next  five  or  six 
letters  of  the  cipher  will  make  sense,  and  thereafter 
the  cipher  offers  no  difficulty. 


—92— 

There  are  numerous  other  methods  of  preparing 
what  is  virtually  a  very  long,  or  even  an  indefinitely 
long  key  from  a  short  key  word,  but  all  such  cipher 
methods  have  the  same  practical  disadvantages  of 
slowness  of  operation  and  difficulty  in  deciphering,  if 
errors  of  enciphering  or  transmission  have  been 
made. 

The  ciphers  of  Napoleon  were  long  series  of 
numbers  representing  letters,  syllables  and  words. 
They  were  really  codes;  and  a  code  based  on  these 
principles,  but  using  letters  instead  of  numerals, 
might  be  evolved  very  easily.  The  War  Department 
Code,  the  Western  Union  Code,  and,  in  fact,  all  codes. 
are  nothing  but  specialized  substitution  ciphers  in 
which  each  code  word  represents  a  letter,  word  or 
phrase  of  the  plain  text. 

Combined  Transposition  and  Substitution  Methods 

It  is  evident  that  a  message  can  be  enciphered 
by  any  transposition  method,  andtheresultenciphered 
again  by  any  substitution  method,  or  vice  versa.  But 
this  takes  time  and  leads  to  errors  in  the  work,  so 
that,  if  such  a  process  is  employed,  the  substitution 
and  transposition  ciphers  used  are  likely  to  be  very 
simple  ones  which  can  be  operated  with  fair  rapidity. 

On  preliminary  determination,  a  cipher  prepared 
by  such  a  combination  of  methods  will  appear  to  be  a 
substitution  cipher  to  be  solved  as  such.  The  fre- 
quency table  of  the  result  will  resemble  the  normal 
frequency  table,  although  the  message  will  still  be 
unintelligible  and  we  will  know  at  once  that  it  is  a 
transposition  cipher  for  further  solution. 

The  substitution  methods  usually  found  in  com- 
bination ciphers  are  those  of  Case  4,  5  and  6,  and  the 
transposition  method  is  nearly  always  Case  1,  and 
particularly  the  simple  varieties  of  this  case  like  the 


—93— 

fence  rail  (Case  1-i),  reversed  writing  or  vertical 
writing. 

A  few  examples  will  show  some  of  the  possible 
combinations. 

The  first  line  of  the  message  of  Case  4-a  is: 

OBQFOBPBRP 

We  might  write  it  BFBBPOQOPR  (Case  1-i), 

or  PRBPBOFQBO  (Case  1,  reversed  writing), 

or  OFQBOPRBPB  (Case  1,  reversed  by  groups  of  five). 

The  first  line  of  the  message  of  Case  2-b  is: 

SLCOF  WEETN  EBRDO  ORVYM  FFEDI 
We  might  write  it  TMDPG  XFFUO  FCSEP  PSWZN  GGFEJ, 
or  RKBNE  VDDSM  DAQCN  NQUXL  EEDCH  (Case  4-a, 
going  forward  one  letter  or  back  one  letter). 

These  examples  give  an  idea  of  the  use  of  com- 
bination methods.  It  is  very  rare  to  find  both  com- 
plicated transposition  and  substitution  methods  used 
in  combination,  If  one  is  complicated,  the  other  will 
usually  be  very  simple;  and  ordinarily  both  are  sim- 
ple, the  sender  depending  on  the  combination  of  the 
two  to  attain  indecipherability.  It  is  evident  how 
futile  this  idea  is. 

Methods  of  Enciphering  Numerals 

It  is  frequently  desirable  to  send  numerals  in 
the  body  of  a  cipher  message.  Several  cipher  sys- 
tems prescribe  that  all  numerals  in  the  body  of  a 
message  must  be  spelled  out;  and,  while  there  is  no 
doubt  but  that  this  insures  greater  accuracy,  it  also 
greatly  increases  the  length  of  such  messages.  In 
most  systems  in  which  it  is  permissible  to  send  numer- 
als, the  following  system  is  used.  An  indicator,  one 
of  the  little  used  letters  and  especially  X,  is  interpo- 
lated before  and  after  the  numeral  or  numerals  to  be 
enciphered,  and  then,  for  each  numeral,  a  letter  is 
substituted  using  this  or  a  similar  table: 

1234567890 
ABCDEFGHIJ 


—94— 

The  enciphering  of  the  message  then  proceeds, 
dealing  with  the  indicator  and  substituted  letters  as 
if  they  were  the  letters  of  a  word.  The  decipherer 
arriving  at  an  X,  a  series  of  the  letters  of  the  above 
table  and  another  X,  casts  out  the  X's  and  substitutes 
numbers  for  the  letters. 

Sometimes  no  indicator  is  used,  but  the  system 
of  substitution  of  a  certain  letter  for  each  numeral 
is  followed.  Again,  the  indicator  NR  may  be  used 
instead  of  a  single  letter. 

Conventional  letters  may  also  be  substituted  for 
special  characters  like  ?,$,",-,  and  periods  and 
commas,  but  this  is  rarely  done  except  for  the  period 
and  question  mark.  The  context  will  usually  de- 
termine the  meaning  of  such  letters  when  found. 
In  this  connection,  the  use  of  X  to  represent  end  of 
a  sentence  and  Q  to  represent  a  question  mark  is 
quite  common. 


Chapter  X 


Errors  in  Enciphering  and  Transmission 

One  of  the  most  difficult  tasks  before  the  cipher 
expert,  is  the  correction  of  errors  which  creep  into 
cipher  texts  in  the  process  of  enciphering  and  trans- 
mission by  telegraph  or  radio. 

In  some  cipher  methods  a  mistake  in  enciphering 
one  letter,  or  the  omission  of  one  letter,  will  so  mix  up 
the  deciphering  process  that  only  one  familiar  with 
such  errors  can  apply  the  necessary  corrections. 

The  transmission  of  cipher  text  over  the  tele- 
graph or  by  radio  is  a  slow  process,  and  many  fairly 
good  operators  cannot  receive  such  matter  satisfac- 
torily, because  they  listen  for  words  and  guess  at 
letters  at  times.  The  spaced  letters  in  American 
Morse  are  the  cause  of  so  many  errors  in  code  trans- 
mission that  the  War  Department  Code  does  not  em- 
ploy any  groups  using  them.  In  fact,  this  code  is 
limited  to  the  letters 

ABDEFGIKMNSTUX 

so  that  there  may  be  a  minimum  of  such  confusion. 
In  cipher  work  it  is  necessary,  under  ordinary 
circumstances,  to  use  any  or  all  of  the  letters  of  the 
alphabet.  To  assist  operators  in  keeping  the  text 
straight,  it  is  customary  to  divide  cipher  text  into 
groups  of  four,  five,  six  or  ten  letters,  and  usually 
groups  of  five  letters  are  used.  The  receiving  opera- 
tor may  then  expect  five  letters  per  group,  and  if  he 
receives  more  or  less  he  is  sure  that  either  he  or  the 
sending  operator  has  made  an  error.  This  division 
into  groups  of  a  constant  number  of  letters  eliminates 
word  forms  and,  in  the  mind  of  the  non-expert,  in- 
95 


—96— 

creases  the  difficulty  of  solving  the  cipher.  But  the 
increase  in  difficulty  is  more  apparent  than  real;  par- 
ticularly, as  a  cipher  examiner  habitually  finds  him- 
self dealing  with  ciphers  without  word  forms,  and 
the  occurrence  of  a  cipher  with  word  forms  usually 
means  that  he  has  an  easy  one  to  handle. 

Messages  are  occasionally  encountered  which 
consist  partly  of  plain  text  and  partly  of  cipher.  The 
cipher  part  may  or  may  not  retain  its  word  forms, 
but,  when  this  method  is  used,  it  is  clearly  impossi- 
ble to  have  a  fixed  number  of  letters  in  each  cipher 
group  if  the  word  forms  are  not  used.  It  is  almost 
impossible  to  prevent  errors  of  transmission  in  such 
messages,  and  it  often  requires  considerable  skill  and 
labor  to  correct  them. 

For  those  unfamiliar  with  the  telegraph  alpha- 
bets, they  are  given  below.  Messages  sent  by  com- 
mercial or  military  telegraphs  or  buzzer  lines  will  be 
transmitted  with  the  American  Morse  alphabet. 
Those  sent  by  radio,  visual  signalling  or  submarine 
cable  will  be  transmitted  by  Continental  Morse, 
known  also  as  the  International  Code.  Messages 
may  be  transmitted  by  both  alphabets  in  course  of 
transmission.  For  example,  a  cablegram  from  the 
Philippines  to  Nome,  Alaska,  will  be  transmitted  by 
Continental  Morse  (commercial  cable)  from  Manila 
to  San  Francisco,  by  American  Morse  (commercial 
land  line)  from  San  Francisco  to  Seattle,  by  Conti- 
nental Morse  (military  cable)  from  Seattle  to  Valdez, 
by  American  Morse  (military  land  line)  from  Valdez 
to  Nulato  and  by  Continental  Morse  (military  radio) 
from  Nulato  to  Nome, 

Prior  to  February,  1914,  the  Mexican  govern- 
ment telegraph  lines  used  an  alphabet  differing 
slightly  from  the  American  and  Continental  Morse. 
However,  at  that  time,  the  Continental  Morse 
alphabet  was  prescribed  for  use  on  these  lines  and 


—97— 

it  is  believed  that  the  use  of  the  old  alphabet  has  en- 
tirely ceased  on   Mexican   lines.     However,    skilled 
American  operators  would  have  no  difficulty  in  pick- 
ing up  this  alphabet  if  it  were  found  to  be  in  use. 
Radio  communication  is,   by   International   Con- 

vention, invariably  in  Continental  Morse. 

. 

Telegraph  Alphabets 

Continental  Morse 
Character  American  Morse         or  International 

Code 
A 
B  -  ...  .... 


E 
F 
G 
H 

j 

K 

L 
M 
N 
O 
P 
Q 
R 
S 
T 
U 
V 

w 

X 

Y 
Z 

1 
2 
3 
4 
5 
6 


—98— 


7 
8 
9 
0 

Period 

Question  Mark 
Comma 


The  following  example  will  show  some  of  the 
errors  that  creep  into  messages  prepared  with  the 
cipher  disk  and  transmitted  by  radio: 

Message 

Radio  Douglas  de  El  Paso,   2  H    71,  twenty-fifth,  9:00  a.m.. 
Govt.     To  C.O.,  Sixth  Brigade,  Douglas,  Arizona: 


JPRZI 

RDJSG 

XTRMJ 

USFPC 

RECLA 

BCPCB 

OAXPK 

QEQKF 

PPZAE 

BKUTT 

JHWEU 

AHPZE 

EZOLT 

HKXPH 

KIHAV 

DRODN 

IAPZC 

LVUMP 

KFUBV 

VTVNV 

EFVZV 

TLVQS 

BKAHQ 

NVKVF 

MGJTH 

OWBGN 

WWEPO 

LJKFP 

HEXKW 

CPDLZ 

JWSQC 

JVKIG 

HTJHT 

EG  AH  A 

GDXXK 

BSPPK 

DIAVZ 

VQONC 

HOVDA 

VZQKW 

FNVON 

RPVGH 

CUFPV 

SFPIE 

TOZOD 

WGYFE 

AWNJY 

KOEDW 

UMELD 

NOBUH 

MUPQL 

GYOPP 

ODBAB 

UFUUC 

AEOJW 

RDIPK 

WMOKV 

OMICW 

CKPIH 

LUMSY 

YOSBG 

WOPHV 

PKOMO 

PHGER 

Smith. 

The  key  word  is  ATCHISON,  the  cipher  disk 
being  used  and  the  setting  changed  for  every  let- 
ter of  the  message.  The  letter  X  indicates  a  period 
where  it  is  evidently  not  a  letter  of  a  word. 

Deciphering  the  message  with  this  key  and 
method  we  have: 


RELIA  BLEIN  FORGF 

RECEI  JLEDHE  RETHA 

EFTTH  ERELA  STNIG 

ARMSA  NDAMM  UNITI 

BORDE  RNEXT  FRIDA 

MIENX  FKOSB 


TIONF  ROMCA  SASGR  ANDES 

TAMOU  NTEDD  ETACH  MSKTL 

HTTOE  SCORT  SHYMP  ENTOF 

ONTOB  ESMUG  GLEDA  CRJXS 

YNIGH  TATAP  OINTT  WELVE 


Beyond  this  point  the  message,  if  we  continue 
the  deciphering  process,  is  unintelligible.  The  sense 
fails  at  the  first  P  of  the  cipher  group  BSPPK.  We 
have  translated  B  as  M  with  disk  A  to  N  and  S  as  I 
with  disk  A  to  A.  The  last  words  that  make  sense 


—99— 

are  A  POINT  TWELVE  MI;  clearly  the  rest  of  the 
last  word  is  LES  and  this  is  represented  by  PPK. 
Putting  P=L  then  A= A  and  putting  P  =  E  then  A= 
T.  In  other  words,  the  encipherer  forgot  to  change 
his  disk  setting,  A  to  A,  after  enciphering  I  into  S 
and  enciphered  L  into  P  with  the  same  setting,  A  to 
A.  Continuing  the  deciphering  on  this  basis,  we 
have: 

LES  EASTO  FDOUG  LAS  .  T  HISIS  INYOU  RDIST 
RICT  .  WILLY  OUTAK  ENECE  SSARV^  STEPS  TOPRE 
VENTTHISSH  IPMEN  TFROM  GOING  SKZRX  LEADE 
ROFSMUGGLE  RSSAL  DTOBE  JUANH  ERNAN  DEZOF 
NACO. 

The  minor  errors  underlined  above  are  not  diffi- 
cult to  correct  except  the  sixth  word  in  the  eighth 
line.  They  will  be  taken  up  however  for  analysis  of 
cause  of  error. 

Line  1,  GF  should  be  MA.  Putting  the  latter 
into  cipher  we  find  the  letters  of  the  cipher  should 
have  been  GO  instead  of  MJ.  This  is  clearly  a  tele- 
grapher's error,  -  -  . becoming  -  -  . 

Line  2,  JL  should  be  V.  The  corresponding  ci- 
pher letter  should  be  F  instead  of  P.  This  is  an 
error  of  the  encipherer  in  copying. 

Line  2,  SK  should  be  EN.  The  corresponding 
cipher  letters  should  be  YU  instead  of  KX.  Another 
telegrapher's  error,  -  .  -  -  .  .  -  becoming  -  .  - 

Line  3,  JY^  should  be  I.  The  corresponding  cipher 
letter  should  be  L  instead  of  V.  Another  error  in 
copying  by  the  encipherer. 

Line  4,  JX  should  be  OS.  The  corresponding 
cipher  letters  should  be  FK  instead  of  KF;  an  error 
on  the  part  of  the  encipherer  in  copying. 

Line  7,  V^  should  be  Y.     A  mistake  in  copying. 

Line  8,  SKZRX.  If  we  take  X  as  a  period,  then 
this  line  might  be  OVER,  the  R  being  correct  and 


—100— 

SKZ  being  in  question.  The  corresponding  cipher 
letters  are  AEO  and  if  we  encipher  OVE  we  get  ETJ. 

Here  again  we  have  a  telegrapher's  error,  .  -  . 

becoming  .  -  . 

Line  9,  J^should  be  I.  The  corresponding  cipher 
letter  should  be  K  instead  of  H;  an  error  in  copying 
by  the  encipherer. 

The  errors  by  the  encipherer  above  noted  are 
fairly  common  ones.  These  and  similar  errors  are 
usually  found  when  a  cipher  message,  prepared  as 
a  rough  draft  by  the  encipherer,  is  copied  by  a  clerk 
and  a  careful  check  of  the  copy  is  not  made.  The 
letters  mistaken  depend,  of  course,  on  the  encipherer's 
hand  writing  or  printing.  Other  errors,  besides 
those  noted,  are  the  confusion  of  C,  G,  and  Q;  I,  and 
J;  B  and  R,  etc. 

The  error  by  the  encipherer,  in  not  changing  his 
disk  setting  for  one  letter  and  thus  throwing  out  the 
whole  process  of  deciphering,  would  not  have  occurred 
had  he  put  the  message  into  eight  columns  or  a  mul- 
tiple thereof  and  enciphered  each  column  with  one 
disk  setting.  This  latter  method  is  also  very  much 
faster. 

Telegraphers'  errors  in  cipher  transmission  are 
common  and  often  very  confusing.  Note  should  be 
taken  as  to  whether  Continental  or  American  Morse 
was  used  for  transmission.  An  analysis  along  the 
lines  indicated  will  usually  develop  the  error  and 
correction.  If  not,  a  repetition  should  be  demanded, 
calling  attention,  if  possible,  to  the  particular  groups 
that  are  not  clear. 

The  deciphered  and  corrected  message  is: 

'  'Reliable  information  from  Casas  Grandes  re- 
ceived here  that  a  mounted  detachment  left  there 
last  night  to  escort  shipment  of  arms  and  ammuni- 
tion to  be  smuggled  across  border  next  Friday  night, 
at  a  point  twelve  miles  east  of  Douglas.  This  is  in 


—101— 

your  district.  Will  you  take  necessary  steps  to  pre- 
vent this  shipment  going  over?  Leader  of  smugglers 
said  to  be  Juan  Hernandez  of  Naco." 

Another  remarkable  example  of  errors  in  trans- 
mission by  American  Morse  is  the  following:  A  mes- 
sage, partly  in  cipher  and  partly  in  plain  text,  con- 
tained the  cipher  words 

GA  GTXIEIT  EIDISXQ 

This,  deciphered  as  far  as  possible  by  the  alpha- 
bet determined  by  analysis  of  the  rest  of  the  cipher, 
read 

SU  SME_Y_M  Y_O_GES 

It  was  finally  decided  that  the  context  required 
a  single  word  like  SUSPENDIO  or  SUSPENDIOLES 
for  this  cipher  group.  An  examination  along  this 
line  showed  that  the  cipher  words  should  have  been 

received GA  GLXCURDPXG 

and  were  received G A  G  T  x  IE  IT  El  D  is  X  Q 

and  that  there  were  five  errors  in  transmission  in 
these  three  cipher  groups  alone. 


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